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:    :':g  S.  t.EE, 

.i-^VilA    COLLi-,.'_ 

New  Yobk, 


Transactions  of  The  Academy  of  Science  of  St.  Louis. 


VOL.  VI.      No.  12. 


THE   GROWTH   OF   ST.   LOUIS   CHILDREN. 


WILLIAM    TOWNSEND    PORTER. 


Issued  April  14,  1894. 


THE  GROWTH  OF  ST.  LOUIS  CHILDREN. 

INTRODUCTION. 

In  November,  1891,  I  applied  to  the  Teachers'  Committee 
of  the  St.  Louis  Board  of  Public  Schools  for  permission  to 
make  a  series  of  physical  measurements  of  the  St.  Louis 
school  children.  The  ends  in  view  were  the  study  of  the 
phenomena  of  growth,  the  making  of  physical  standards  for 
each  age  in  the  period  of  school  life,  and  the  adjustment  of 
school  tasks  to  the  pupil's  strength.  On  the  recommendation 
of  Mr.  Long,  superintendent  of  the  Public  Schools,  Dr.  Hick- 
man and  Mr.  Walter  F.  McEntire,  at  that  time  chairman  of 
the  committee,  it  was  resolved  to  lay  before  the  Board  a 
statement  of  the  purpose  of  the  measurements  and  to  advise 
that  the  permission  to  make  them  be  granted.  This  favorable 
report,  for  which  thanks  are  due  the  gentlemen  just  named, 
caused  the  Board  to  authorize  the  measurements  at  its  sitting 
December  8,  1891. 

The  measurements  were  collected  by  what  statisticians  know 
as  the  generalizing  method.  In  the  generalizing  method,  a 
great  number  of  children  is  measured  once,  and  the  measure- 
ments classified  according  to  age.  The  mean  height  of  the 
boys  or  girls  at  each  age  is  regarded  as  the  height  typical 
of  that  age.  When  these  typical  heights  are  arranged 
in  order,  they  show  the  increase  in  the  height  of  the  type- 
child  during  his  period  of  growth  and  thus  express  a 
law  of  growth.  A  similar  procedure  reveals  the  growth  in 
■weight,  girth  of  chest,  or  any  other  physical  dimension.  It  is 
believed  that  the  values  got  by  the  generalizing  method  are 
the  same  as  would  be  obtained  if  a  smaller  number  of  children 
was  measured  yearly  during  the  growth  period.  In  either 
case,  the  accuracy  of  the  result  depends  on  the  number  of 
observations  at  each  age,  and  a  high  degree  of  accuracy 
requires  the  making  of  many  thousand  measurements. 

(263) 


264  Introduction. 

So  large  an  undertaking  demands  great  labor  and  a  consid- 
erable expenditure  of  money.  The  labor  was  in  the  present 
instance  shared  by  many  hands.  Most  of  the  measurements 
were  made  by  the  teachers.  The  measurements  of  the  head 
and  face  were  made  by  undergraduates  of  the  St.  Louis 
Medical  College.  Other  members  of  the  same  institution 
were  of  the  greatest  service  as  "  special  assistants."  Messrs. 
Taussig,  Gooden,  Soper,  Blair,  Gross,  Schlossstein,  Lemen, 
Loth,  Newcomb  and  Simmons  served  in  this  capacity. 
To  their  unwearied  and  long-continued  labors  and  to  the 
support  unselfishly  given  them  by  their  fellow-students  the 
success  of  the  work  is  chiefly  due. 

The  expense  of  the  investigation  was  for  apparatus,  printing 
and  the  hire  of  clerks,  and  was  borne  by  gentlemen  of  public 
spirit  in  St.  Louis.  Some  of  the  apparatus  was  given  or 
loaned  free  of  charge.  The  Simmons  Hardware  Company 
gave  callipers  and  measuring  tapes  ;  the  Fairbanks  Scale  Com- 
pany loaned  scales;  Mr.  F.  W.  Humphrey  loaned  a  dozen 
watches;  Dr.  John  Green  and  Dr.  A.  E.  Ewiug  gave  cards 
for  testing  the  acuteness  of  vision,  and  the  Nixon- Jones 
Printing  Company  made  special  rates  for  printing. 

The  cordial  support  of  Chancellor  Chaplin,  Professors  H. 
S.  Pritchett,  G.  Hambach  and  E.  A.  Engler  of  Washington 
University,  the  valuable  advice  of  Dr.  John  B.  Shapleigh,  and 
the  interest  of  the  Academy  of  Science  of  St.  Louis  are 
gratefully  acknowledged. 

The  data  collected  are  necessarily  of  unequal  value.  Many 
of  the  curves  constructed  from  them  are  highly  satisfactory; 
others  present  irregularities  to  be  ascribed  to  an  insufficient 
number  of  observations  at  those  points.  Some  investigators 
have  withheld  the  curves  in  which  such  irregularities  occur. 
They  have  all  been  printed  here,  because  the  wide-spread  use 
of  anthropometrical  methods  in  the  Public  Schools,  so  much 
to  be  desired,  seems  at  present  only  possible  where  the  meas- 
urements are  made  by  the  teachers,  and  it  is  necessary  to 
know  by  the  examination  of  the  total  material  of  such  inves- 
tigations, what  degree  of  accuracy  can  be  expected. 


CHAPTER  J. 

THE  COLLECTION  OF  THE  MEASUREMENTS. 

In  collecting  anthropometrical  measurements  on  a  large 
scale,  a  systematic  working-plan  is  evidently  of  much  impor- 
tance. Many  things  should  be  borne  in  mind  in  making  such 
a  plan.  The  school  routine  should  be  disturbed  as  little  as 
possible ;  the  directions  to  the  measurers  should  be  compre- 
hensive and  clear;  the  apparatus  employed  should  be  simple; 
the  measurements  should  be  made  during  a  few  months  only 
and  in  the  same  season  of  the  year,  for  the  weight  of  clothing 
and  even  the  rate  of  growth  differs  at  different  seasons,  and 
measurements  collected  partly  in  one  season  and  partly  in  an- 
other cannot  be  so  suitable  for  comparison  as  those  collected 
only  in  the  winter  or  only  in  the  summer;  the  order  in  which 
the  schools  are  visited  should  be  governed  by  their  situation,  so 
that  no  time  may  be  spent  unnecessarily  in  going  and  coming ; 
and  much  care  should  be  taken  to  collect  sufficient  data  con- 
cerning the  social  condition  and  the  nationality  of  parents. 
In  short,  the  construction  of  a  serviceable  working-plan  for 
anthropometrical  measurements  of  great  numbers  of  children 
is  a  difficult  task,  and  it  is  to  be  regretted  that  the  literature 
is  all  but  barren  of  suggestions  as  to  the  best  method  of 
collecting  such  material.  It  is  hoped  for  this  reason  that  a 
description  of  the  methods  used  in  this  investigation  may  be 
not  without  value. 

The  data  collected  are  mentioned  in  Form  A.,  one  of  four 
"  forms"  employed  in  this  investigation. 

Form  A. 

MALE, 

Please  Write  with  Ink. 

-1.  Observer 

2.  School 

3.  Date 

4.  Name  of  pupil 

5.  Place  of  birth 

6.  Age  at  nearest  birthday 

(265) 


266  Trans.  Acad.  Sci.  of  St.  Louis. 

7      In  what  country  was  father  born  

8.  In  what  country  was  mother  born > 

9.  Occupation  of  father 

10.  No.  of  sisters  living ;  dead 

11.  No.  of  brothers  living ;  dead 

]  2.     Residence,  No Street. 

fDark  Brown. 
Dark  Brown.  ...  ,  ^  _ 

„  I  Light  Brown. 

13.     Hair  ■{  Light  Brown.  U.     Eyes     -{     r^^ 

I  Red.  „ 

^,  I  Grey. 

I  Flaxen.  L        •' 

15.  Height  standing cm. 

16.  Height  sitting cm. 

17.  Span  of  arms cm. 

18.  Strength  of  squeeze,  right  hand lbs. 

19.  Strength  of  squeeze,  left  hand lbs. 

20.  Girth  of  chest,  forced  expiration cm. 

21.  Girth  of  chest,  forced  inspiration cm. 

22.  Weight lbs. 

23.  Acuteness  of  vision,  right  eye 

24.  Acuteness  of  vision,  left  eye 

25.  Acuteness  of  hearing,  right  ear ft in 

26.  Acuteness  of  hearing,  left  ear ft in. 

27.  Length  of  head mm. 

28.  Width  of  head mm. 

29.  Height  of  face mm. 

30.  Width  of  face mm. 

31.  The  height  of  face  from  the  hair  line  to  ihe  point  of  chin mm. 

32.  Grade 


Form  B  was  the  same  as  Form  A,  except  that  the  paper  ou 
which  it  was  printed  was  green  instead  of  white,  the  color  of 
Form  A,  and  the  word  "Male"  was  replaced  by  the  word 
"  Female." 

On  Jan.  4,  1892,  the  first  school  *  in  the  series  to  be  exam 
ined  began  to  set  down  the  answers  1,  2,  3,  4,  13, 14,  32,  and 
its  pupils  were  directed  to  carry  home  Form  C  in  order  that 
it  might  be  filled  by  the  parents. 


*  Pupils  were  measured  in  the  following  schools:  Ames,  Blair,  Blow, 
Branch  High,  Bryan  Hill,  Carr,  Carroll,  Carr  Lane,  Central  High,  Charless, 
Chouteau,  Clay,  Clinton,  Crow,  Divoll,  Douglass,  Eliot,  ElleardsvilJe,  Frank- 
lin, Garfield,  Hamilton,  Hodgen,  Humboldt,  Irving,  Jackson,  Jefferson, 
Laclede,  Lafayette,  Lincoln,  Lowell,  Lyon,  Madison,  Maramec,  Mullanphy, 
O'Fallon,  Peabody,  Penrose,  Pestallozzi,  Polytechnic,  Pope,  Shepard,  Shields, 
Spring  Avenue,  Stoddard,  Webster,  New  Webster.  (The  "  Branches  "  of 
the  Clinton  and  other  schools  are  included.) 


Porter  —  The  Growth  of  St.  Louis  Children.  267 

Form  C. 

THE   PHYSIQUE    OF   THE   SCHOOL   CHILDREN  IN   ST.    LOUIS. 

The  parents  or  guardians  of  school  children  are  requested  to  fill  out  the 
following  blank,  and  to  return  it  to  the  teacher  on  the  next  school  day : 

4.  Name  of  pupil 

5.  Place  of  birth 

6.  Age  at  nearest  birthday 

7.  In  what  country  was  pupil's  father  born 

8.  In  what  country  was  pupil's  mother  born 

9.  Occupation  of  father 

10.  Number  of  pupil's  sisters  living ;  dead 

11.  Number  of  pupil's  brothers  living ;  dead 

12.  Eesidence  of  pupil,  No , Street. 

On  the  second  day,  Form  C  having  been  returned,  answers 
5,  6,  7,  8,  9,  10,  11  and  12  were  written.  Some  ignorant  or 
prejudiced  parents  refused  to  answer  the  questions  in  Form  C 
and  in  such  cases  the  answers  were  obtained  as  far  as  possible 
from  the  school  registers.  While  the  first  school  was  em- 
ployed in  this  way  on  the  second  day,  another  school  began 
to  answer  questions  1,  2,  3,  4  and  32.  On  the  third  day,  the 
first  school  measured  the  height  standing,  height  sitting  and 
span  of  arms,  while  the  second  school  was  busy  with  the 
second  day's  work  and  the  third  school  with  the  first. 

Thus  the  thirty-two  questions  were  divided  into  groups,  and 
by  the  ninth  day  nine  schools  were  working  simultaneously, 
each  on  a  different  group.  As  soon  as  one  school  finished 
with  an  apparatus,  it  was  taken  to  the  next  school  on  the  list, 
almost  always  the  nearest  in  point  of  distance.  An  extract 
from  "  The  Chart  of  Days  "  will  make  this  clear. 


268 


Trans.  Acad.  Sci.  of  St.  Louis. 


A    PORTION    OF     "  THE    CHART    OF    DAYS.' 


NAME    OF 
SCHOOL. 


SPECIAL 
ASSISTANT. 


Record : 

MS 

M  to 

"^ 

"la 
..a 

o 

CD 

N 

a> 

0) 

3 

J3 

o 

O 

bo 
a 
'S 

ei 

w 

o 

m  O 

00 

bo  33 

O 
o 

S 

_bp 
'S 

tn 

<o 
a 

CO 

0) 

a 

flO 

fl 

a> 

03 

« 

o 

<J^ 

< 

tn 

5 

< 

<! 

Laclede 

Madison  and  New 
Madison 

Pestalozzi 

Carroll 

Lafayette  and  La- 
fayette Branch.. 

Humboldt 

Lyon 

Shepard 

Meramec 

Blow  and  Blow 
Branch  


Lemen 

Simmons.  .- 
Newcomb... 
Loth 

Taussig. .. . 
Gooden  . ... 

Soper 

Blair... 

Gross 

Schlossstein 


4* 

5 

7 

8 

11 

12 

13 

14 

5 

6 

8 

11 

12 

13 

14 

15 

6 

7 

11 

12 

13 

14 

15 

18 

7 

8 

12 

13 

14 

15 

18 

19 

8 

11 

13 

14 

15 

18 

19 

20 

11 

12 

14 

15 

18 

19 

20 

21 

12 

13 

15 

18 

19 

20 

21 

22 

13 

14 

18 

19 

20 

21 

22 

25 

14 

15 

19 

20 

21 

22 

25 

26 

15 

18 

20 

21 

22 

25 

26 

27 

18 
19 
20 

21 
22 

25 
26 
27 


The  Laclede  School  began  Jan.  4  and  finished  Jan.  15,  the 
Madison  School  began  Jan.  5  and  finished  Jan.  18,  and  so 
through  the  list. 

Nearly  nine  thousand  pupils  were  examined  each  school-day 
after  the  ninth,  and  each  day  saw  the  returns  of  nearly  a 
thousand  pupils  completed.  The  collection  of  material  was 
finished  in  fifty-four  school-days,  beginning  Jan.  4  and  ending 
March  18.  During  this  period  of  about  11  weeks,  18059 
girls  and  16295  boys  were  examined  f  and  nearly  one  million 
data  collected,  about  five  hundred  thousand  of  which  were 
measurements,  a  result  which  would  hardly  have  been  possible 
without  the  strenuous  exertions  of  my  assistants. 

One  of  the  Special  Assistants  mentioned  in  the  Chart  of 
Days  was  assigned  to  each  school  under  investigation.  It  was 
his  duty  to  visit  the  school  every  day  for  the  purpose  of 
giving  any  explanation  which  might  be  necessary.     He  was 


*  This  and  the  following  numbers  are  the  days  of  the  month  on  which  the 
respective  groups  of  measurements  were  made. 

t  Owing  to  absentees,  the  number  of  returns  of  any  one  measurement, 
e.  g.,  height,  was  less  than  the  number  here  given. 


Porter  —  The  Growth  of  St.  Louis  Children.  269* 

charged  also  to  see  that  his  school  finished  its  allotted  daily 
task  and  dispatched  at  the  close  of  the  session  the  apparatus 
in  its  hands  to  the  next  school  on  the  list.  In  addition  to 
these  nine  Special  Assistants,  thirty  Head  Measurers  were 
employed.  The  Head  Measurers  were  divided  into  five  sec- 
tions named  after  the  days  of  the  school  week  from  Monday 
to  Friday.  Each  section  went  on  its  own  day  to  the  school 
whose  turn  it  was  to  have  heads  and  faces  measured.  The 
remaining  measurements  were  made  by  the  teachers. 

Not  even  the  industry  of  these  many  assistants  would  have 
accomplished  the  task  in  the  required  time  had  there  not  been 
an  abundance  of  apparatus.  Of  measuring-rods,  measuring- 
tapes  for  the  chest,  double  sets  of  Snellen-Green  test  letters, 
spectacle  blinders,  watches  and  callipers,  there  were  a  dozen 
each,  and  five  dynamometers  and  six  small  platform-scales 
were  also  in  constant  use.  Twelve  school  rooms  could  thus 
often  work  at  the  same  time,  and  a  great  many  children  were 
measured  in  a  few  hours. 

The  following  printed  instructions  were  given  to  every 
measurer. 

Form  D. 

INSTRUCTIONS  TO  OBSERVERS. 

Four  printed  forms  are  furnished.    Tliese  are : 
Form  A.     Male  (wliite  paper) . 
"     B.     Female  (tinted  paper) . 
"      C.    For  parents. 
"      D.  Instructions  to  observers. 

On  Monday,  January  4th,  a  sufficient  number  of  these  forms  will  be  taken 
to  school  A.  The  same  day  answers  1,  2,  3,  4, 13, 14  and  32,  Form  A  or  B,  are 
written,  and  each  pupil  is  given  Form  C  to  carry  home.  The  next  morning 
form  C  is  returned  by  the  pupils,  and  answers  5,  6,  7,  8,  9,  10,  II  and  12 
are  copied  on  form  A  or  B.  The  third  day  the  measurements  begin,  and  are 
carried  out  according  to  the  following 


CALENDAR 

Ist^ 

day 

1,: 

2,3, 

4, 

13, 

14, 

32. 

2d 

5,' 

6,7, 

|8, 

9,: 

10, 

11, 

12. 

3d 

15, 

16, 

17 

4th 

18, 

,  19. 

5th 

20, 

,  21. 

6th 

22. 

7th 

23, 

24. 

8th 

25, 

,  26. 

9  th 

27, 

28, 

29, 

,  30 

,31 

. 

270  Trans.  Acad.  Sci.  of  St.  Louis. 

Form  C  and  answers  1  to  12  in  forms  A  and  B,  require  no  explanation. 
Ttie  remaining  answers  are  to  be  sought  by  the  following  methods. 

Arrange  forms  A  and  B  in  the  order  in  which  the  pupils  sit  at  their  desks, 
and  preserve  this  arrangement  throughout  the  measurements. 

13,  14.   Color  of  Hair  and  Eyes. 

Choose  the  adjective  that  most  nearly  indicates  the  color;  cross  out  the 
rest  with  pen  and  ink. 

13.  Height  Standing. 

1.  All  the  pupils  unlace  their  shoes. 

2.  The  teacher  places  the  measuring  rod  against  the  cloak-room  door  cas- 
ing, the  projections  on  the  rod  serving  to  keep  it  parallel  with  the  casing, 
and  presumably  perpendicular  to  the  floor. 

3.  The  pupil  in  the  first  seat  comes  forward,  removes  his  shoes,  stands 
on  a  folded  newspaper  upon  which  the  rod  also  rests,  his  heels,  body  and 
head  touching  the  door  casing,  the  mouth  closed  and  the  chin  somewhat 
depressed.    Hair  worn  in  a  high  knot  must  be  let  down. 

4.  Lower  the  sliding  arm  until  the  edge  touches  the  crown  of  the  pupil's 
head,  and  dictate  the  reading  to  a  pupil  assistant,  who  writes  it  opposite 
"15.  Height  standing."  Meanwhile,  the  second  pupil  gets  ready.  [The 
rods  are  divided  in  centimetres  and  half  centimetres;  it  will  be  easy  to  read 
to  quarter  centimetres.  The  dictation  should  be  in  the  decimal  system; 
thus:  "  One  hundred  fifteen,  seventy-five  (written  115.75), not  one  hundred 
fifteen  and  three  quarters.] 

5.  The  first  pupil  steps  to  one  side,  puts  on  his  shoes,  returns  to  his  seat, 
and  there  laces  his  shoes.  The  second  pupil  removes  his  shoes  and  steps 
on  the  newspaper.    The  third  pupil  comes  forward. 

1 6.  Height  Sitting. 

Place  an  armless  wooden  chair  with  a  flat  seat  sideways  against  the  door 
casing.  The  measuring  rod  is  held  perpendicularly  on  the  seat,  the  pro- 
jections on  the  rod  touching  if  possible  the  casing.  Pupils  come  forward 
as  before. 

Take  care:  1,  that  the  lower  part  of  the  spinal  column  touches  the  rod; 
2,  that  the  mouth  is  closed  and  the  chin  somewhat  depressed ;  3,  that  hair 
worn  in  a  knot  on  the  back  of  the  head  does  not  introduce  an  error.  Meas- 
ure, and  dictate  the  reading. 

2  7.  Span  of  Arms. 

1.  Draw  on  the  wall  a  chalk  mark  parallel  with  the  floor  and  as  high  as 
the  chin  of  a  pupil  of  average  height. 

2.  Hold  the  measuring  rod  parallel  to  the  line  and  as  high  as  the  neck  of 
the  pupil  to  be  measured. 

3.  The  pupil  touches  one  end  with  the  middle  finger  of  one  hand  and 
stretches  along  the  rod  as  far  as  he  can  reach;  chin  up,  heels  together,  body 
as  close  as  possible  to  the  rod. 

4.  Dictate  the  reading. 

[In  this  and  all  other  measurements  the  place  of  the  pupil  measured 
should  be  instantly  taken  by  another.  ] 


Porter  —  The  Growth  oj  St.  Louis  Children.  271 

18,  19.  Strength  of  Squeeze. 

1.  Depress  tlie  trigger  of  the  dynamometer  until  the  point  of  the  indicator 
is  exactly  over  the  zero  line  of  the  scale. 

2.  The  pupil  grasps  the  oval  ring  in  the  right  hand  and  squeezes  his 
best. 

3.  Read  the  outer  scale  (graduated  from  0  to  160)  to  pounds  *  as  ex- 
actly as  possible.  Write  the  number  after  <'  18.  Strength  of  Squeeze,  right 
hand." 

4.  Reset  the  instrument,  and  test  left  hand.  [Please  do  not  touch  the 
indicator.    Always  use  the  trigger.] 

20,  21.   Girth  of  Chest. 

1.  Take  four  pupils  into  the  cloak  room.  They  remove  clothing  over 
chest  down  to  the  garment  next  the  skin.  The  measurements  are  made  on  a 
level  with  the  nipples,  and  are  dictated  in  centimetres  and  decimal  frac- 
tions of  a  centimetre  to  a  pupil  assistant,  who  writes  them  opposite  20 
and  21. 

2.  "Forced  expiration."  Pupil  breathes  out,  makes  chest  as  small  as 
possible,  inclines  head  forwards,  draws  shoulders  slightly  together. 

3.  "Forced  inspiration."  Shoulders  back,  head  raised,  deepest  possible 
inspiration. 

.  [Some  children  will  require  to  be  shown  how  to  do  this.  As  fast  as  a  pupil 
is  measured,  dresses  and  returns  to  his  seat,  another  pupil  enters  the  cloak 
room  to  take  his  place,  and  strips  for  measurement.] 

22.  Weight. 
The  upper  figures  on  the  beam  and  the  smaller  of  the  two  numbers  on  the 
iron  weights  are  used  with  the  scale  pan.  Pay  no  attention  to  them.  The 
lower  figures  on  the  beam  read  from  1  to  45  pounds.  Place  the  pupil's 
approximate  weight  on  the  counterpoise  at  the  end  of  the  beam ;  move  the 
poise  along  the  latter  until  the  scale  balances.  Add  the  larger  number  on 
the  hanging  weight  to  the  number  marked  on  the  lower  scale  by  the  poise. 
The  sum  is  the  pupil's  weight. 

23,  24:.  Acuteness  of  Vision. 

It  is  necessary  to  make  these  tests  between  10:30  a.  m.,  or  better  11 
a.  m.,  and  3  p.  m.,  as  at  other  hours  the  winter  light  is  insufficient. 

A  pupil  must  not  see  the  card  before  the  moment  for  his  test  has  come. 
Nor  can  the  pupils  who  have  been  tested  be  allowed  to  communicate  with 
those  yet  to  be  tested.  Otherwise  the  letters  will  be  committed  to  memory 
and  the  test  spoiled. 

1.  Hang  the  test  card  on  the  wall  opposite  the  windows,  in  a  good  light, 
and  level  with  the  pupil's  eyes.  Turn  down  the  middle  leaf  of  the  card,  so 
that  only  one  set  of  test  letters  is  visible. 

2.  Stand  the  pupil  with  toes  touching  a  chalk  mark  16  feet  5  inches  from 
the  card,  and  cover  the  left  eye  with  the  blinder  furnished  for  that  purpose . 
The  head  must  be  held  straight,  so  that  the  child  cannot  see  the  test  letters 
with  the  blinded  eye. 


wo  dynamometers  were  graduated  metrically. 


272  Trans.  Acad.  Sci.  of  St.  Louis. 

3.  The  child  reads  the  test  letters  beginning  with  the  largest ;  the  smallest 
letter  which  can  be  read  indicates  the  "  acuteness  of  vision  "  at  16  feet  5 
inches  (5  metres).  Mark  the  arable  figure  under  this  letter  opposite 
"  Acuteness  of  Vision,  right  eye." 

4.  Change  the  blinder  to  the  right  eye. 

5.  Turn  up  the  middle  leaf  of  the  test  card  so  as  to  expose  the  second  set 
of  test  letters . 

6.  Test  the  acuteness  of  vision  of  the  left  eye  in  a  similar  manner. 

25,  26.  Acuteness  of  Hearing. 
The  hearing  tests  are  to  be  made  in  the  cloak-room  with  the  doors  closed. 
Their  success  depends  primarily  on  the  absence  of  all  noise  from  the  adjacent 
class-rooms  and  halls. 

1.  The  pupil  is  seated  with  the  right  ear  towards  the  observer. 

2.  An  assistant  closes  the  pupil's  left  ear  by  pressing  the  tragus  (the  little 
cartilage  in  front  of  the  external  opening)  inwards  with  her  thumb  while 
with  the  fingers  of  the  same  hand  she  closes  the  eyelids  with  a  handkerchief. 
"With  the  other  hand  the  assistant  holds  the  end  of  the  brass  ring  of  the  tape 
measure  against  the  head  just  beneath  the  ear,  grasping  the  ring  between 
thumb  and  forefinger  and  keeping  the  hand  entirely  below  the  auditory 
opening. 

3.  The  observer  stands  directly  opposite  the  ear  and  11  feet  from  it, 
holding  the  tape  parallel  with  the  floor.  The  watch  is  held  by  the  chain 
ring  against  the  median  line  of  the  observer's  body,  just  above  and  not 
touching  the  tape.    The  face  of  the  watch  is  towards  the  pupil. 

4.  The  observer  charges  the  pupil  to  say  "  now  "  when  he  hears  the 
watch  tick,  and  advances  the  watch  until  the  pupil  replies.  The  watch  is 
now  withdrawn  and  again  advanced  until  the  pupil  replies.  Marking  this 
point  on  the  tape  measure  between  finger  and  thumb,  the  observer  puts  the 
watch  behind  her  back,  and  asks  '«  Do  you  hear  now?  "  If  the  pupil  replies 
"  No,"  the  watch  is  returned  to  the  former  position  and  the  inquiry  repeated. 
If  the  watch  is  again  heard  at  this  distance  the  test  is  satisfactory ;  if  not, 
it  should  be  repeated.  "Write  the  distance  at  which  the  watch  is  heard  in 
feet  and  inches  opposite  "Acuteness  of  Hearing,  right  ear." 

5.  Turn  the  pupil  around  (180°)  and  test  the  left  ear  in  a  similar  manner. 
The  wilfulness  of  some  children  will  make  the  accuracy  of  their  tests 

doubtful.     In  such  cases  write  an  interrogation  mark  after    the    figures 
secured. 

27,  28,  29,  30.  Head  Measurements. 
The  teacher  carries  the  blanks  arranged  in  the  order  in  which  the  pupils 
sit  in  her  room,  a  pen,  and  a  centimetre  rule.  The  medical  assistant  makes 
a  measurement,  places  the  callipers  on  the  rule  which  the  teacher  holds, 
and  reads  the  number  of  centimetres  and  millimetres.  The  teacher  writes 
these  numbers  while  the  assistant  makes  the  next  measurement. 

Instructions  for  Medical  Assistants. 

Measurements  must  be  read  to  millimetres. 

1.  Length  of  head.  —  Place  one  point  of  the  callipers  on  the  most  prominent 
point  of  the  forehead,  between  the  eyebrows.  Bring  the  other  point  of  the 
callipers  down  to  the  posterior  part  of  the  head  and  move  it  along  the  middle 
line  until  the  greatest  length  of  the  head  is  found.     (A,  B.) 


Porter —  The  Growth  of  St.  Louis  Children. 


273 


2.  Breadth  of  head.  —  Take  the  greatest  breadth  of  the  head  between  the 
ears  wherever  it  is  found.  Hold  the  callipers  horizontally  and  perfectly 
symmetrically,  approximately  at  F. 

3.  Height  of  face. —  Put  one  point  of  the  callipers  in  the  deepest  depression 
on  the  nose  between  the  eyes  (C)  —  then  press  the  other  point  against  the 
chin  and  find  that  point  at  D  where  the  chin  turns  backwards.  Ask  the  per- 
son to  press  his  teeth  together. 

4.  Breadth  of  face. —  This  is  the  greatest  breadth  between  the  narrow,  bony 
ridges  felt  in  front  of  the  ears.  The  ridges  ran  from  the  cheek  bones  to  the 
ears.  Hold  the  callipers  horizontally  and  symmetrically,  approximately 
atG. 


Position  of  the  Points  at  which  Head  Measurements  are  Taken. 
A-B,  length  of  head.    Approximately  at  F,  breadth  of  head.     C-D,  Height 
of  face.    Approximately  at  G,  breadth  of  face.* 

6.  Hair  line.  —  This  is  the  height  of  face  from  the  point  of  the  chin  to  the 
point  where  the  hair  begins  to  grow  above  the  forehead. 

Further  information,  if  desired,  may  be  had  by  addressing  the  Physiolog- 
ical Laboratory  of  Washington  University,  625  Clark  avenue. f 

"W.  TowNSEND  Porter. 
Approved  Jan.  4th,  1891. 
E.  H.  Long, 

Superintendent. 

Some  changes  were  made  ia  the  above  instructions  during 
the  course  of  the  investigations.  The  tests  of  acuteness  of 
hearing  were  found  impracticable  because  of  the  unavoidable 
noise  in  the  schools  and  were  given  up  after  about  seven 
thousand  pupils  had  been  tested.  It  was  noticed  that  the 
number  possessing  less  than  the  normal  acuteness  of  hearing 
was  very  large,  and  more  than  one  pupil  was  found  who  had 
been  punished  for  inattention,  the  result  of  an  unsuspected 


*  I  am  indebted  to  Dr.  Franz  Boas  for  this  figure. 

t  Since  removed  to  1806  Locust  street.     Dr.  Porter's  present  address  is 
Harvard  Medical  School,  Boston,  Mass. 


274  Trans.  Acad.  Sci.  of  St.  Louis. 

deafness.  Although  the  returns  did  not  seem  sufficiently 
trustworthy  for  statistical  treatment,  they  justified  the  state- 
ment that  not  a  little  deafness  exists  unknown  to  both  teacher 
and  parents.  This  hidden  infirmity  deprives  the  pupil  of 
much  of  the  benefit  of  class-room  instruction. 

The  measurement  of  the  girth  of  chest  over  the  garment 
next  the  skin  was  also  modified  after  several  thousand  boys 
and  girls  had  been  measured,  and  the  boys  were  made  to  re- 
move coats  and  vests  while  the  girls  were  measured  over  the 
indoor  dress.     The  few  girls  who  wore  stays  laid  them  aside. 


CHAPTER    II. 

THE   STATISTICAL   METHODS   EMPLOYED. 

All  measurements  are  accompanied  by  unavoidable  errors. 
Thus  the  attempt  to  measure  the  height  of  a  man  is  influenced 
by  the  accuracy  with  which  the  measuring  apparatus  is  con- 
structed, the  care  with  which  it  is  used,  the  position  of  the 
man's  head  on  the  vertebral  column,  the  thickness  of  the 
interveitebral  disks  and  a  multitude  of  other  factors.  Some 
of  these  influences  would  make  the  observed  height  greater 
than  the  true  height,  others  would  make  it  less.  The  one 
group  tends  to  counteract  or  compensate  the  other,  and  the 
result  of  their  conflict  is  the  measurement  actually  observed. 
The  observed  height  therefore  is  never,  except  by  chance,  the 
real  height,  but  deviates  from  it  in  one  or  the  other  direction  — 
is  now  above  and  now  below  the  truth  —  as  one  or  the  other 
group  of  influences  gets  the  upper  hand.  The  greater  the 
number  of  influences,  the  more  perfectly  does  compensation 
take  place  and  the  more  nearly  does  the  observed  result 
approach  the  truth.  But  the  truth  itself  can  never  be  known, 
for  only  when  the  number  of  influences  is  infinite,  can  the 
probability  of  perfect  compensation  between  them  rise  to  a 
certainty.  That  which  we  call  true  is  merely  the  probable 
truth  and  is  worthy  of  confidence  in  exact  proportion  to  its 
numerical  probability. 

The  influences  which  affect  a  measurement  are  of  two  sorts, 
the  one  accidental  and  varying,  such  as,  taking  the  measure- 
ment of  height  for  an  example,  the  degree  of  inclination  of 
the  head  to  the  axis  of  the  body,  the  placing  of  the  measuring- 
rod  and  the  like,  the  other  constant  and  unvarying,  such  as  an 
inaccuracy  in  the  construction  of  the  measuring-rod  or  a  per- 
sistent bias  in  the  mind  of  the  observer.  In  both  classes,  the 
degree  of  compensation  varies  with  the  number  of  influences, 
for  even  a  constant  cause,  although  not  accidental  in  its  nature 
and  found  always  on  one  side  of  the  mean,  may  be  compen- 
sated by  another  constant  cause  on  the  opposite  side  of  the 

(275) 


276  Trans.  Acad.  Sci.  of  St.  Louis. 

mean.  The  accidental  or  varying  influences,  however,  are 
much  more  numerous  than  the  constant  or  unvarying,  and 
thus  compensation  is  in  their  case  much  more  complete. 
Constant,  unvarying  influences  are  therefore  more  deceptive 
than  varying,  accidental  influences. 

In  practice,  the  influences  determining  the  result  of  a  single 
measurement  elude  all  attempts  at  calculation,  and  the  extent 
to  which  the  result  of  a  single  observation  approximates  the 
truth  cannot  be  told.  But  if  many  measurements  are  made 
of  the  same  thing,  for  example  the  height  of  a  man,  the 
individual  measurements  arrange  themselves  on  either  side  of 
the  true  height.  If  only  accidental  influences  have  been  at 
work  in  each  individual  measurement  in  the  series,  the  dis- 
tribution of  the  observed  heights  on  either  side  of  the  real 
height  would,  if  the  number  of  observations  were  infinite,  be 
symmetrical.  Thus  the  true  height  would  at  once  appear,  and 
the  probability  or  degree  of  deviation  of  any  single  measure- 
ment would  also  be  visible.  Even  with  finite  numbers  a 
probability  so  great  as  to  amount  to  a  practical  certainty  can 
be  secured.  If  2,000  measurements  of  the  same  physical 
dimension,  e.  g.  the  height  of  an  individual,  are  made  care- 
fully, the  total  number  of  observations  will  be  distributed 
nearly  as  follows  :  — 


Porter  —  The  Growth  of  St.  Louis  Children, 


277 


TABLE  No.  1. 

The  Distribution  of  2,000  Measurements  of  the  Same  Quantity  when 
THE  Deviation  of  the  Individual  Observations  From  the  Trub 
Value  of  the  Measured  Quantity  is  due  to  Purely  Accidental 

Causes.* 


d  =  the  Probable  Deviation. 

Number  of  Observations. 

Greater  than  +  5.0  d 

1 

+  4.5  d  to 

+  5.0  d 

1 

+  4.0  d 

+  4.5  d 

5 

+  3,5  d 

+  4.0d 

11 

+  3.0d 

+  3.5d 

25 

-j-  2.5  d 

+  3.0d 

49 

+  2.0  d 

+  2.5  d 

85 

-\-l.5d 

+  2.0d 

135 

+  1.0  d 

+  1.5  d 

188 

+  0.5d 

+  l.Od 

236 

±   .0 

+  0.5  d 

264 

—  0.5d 

d=    .0 

264 

—  l.Od 

—  0.5  d 

236 

—  1.5  d 

—  l.Od 

188 

—  2.0d 

—  1.5  d 

135 

—  2.od 

—  2.0d 

85 

—  B.Od 

—  2.5d 

49 

—  3.5  d 

—  3.0d 

25 

—  4.0d 

—  S.5d 

11 

—  i.od 

—  4.0d 

5 

—  5.0d 

—  4.5d 

1 

Greater  than 

—  5.0  d 

1 

This  result  is  quite  independent  of  the  nature  of  the  thing 
measured,  provided  that  no  unvarying  influences  are  at  work. 

An  examination  of  Table  No.  1  shows  (1)  that  the  distribu- 
tion of  the  observations  is  symmetrical  about  a  median  point, 
in  other  words  that  equal  deviations  to  one  and  the  other  side 
of  this  point  are  equally  probable  ;  (2)  that  half  the  whole 
number  of  observations  fall  within  ±  1.0  cZ  of  the  most  prob- 
able value,  indicating  that  a  small  deviation  is  more  probable 
than  a  large  one;  and  (3)  that  there  is  a  limit  beyond  which 
no  deviation  occurs.  Such  are  the  peculiarities  of  a  series  of 
observations  in  which  the  deviations  from  the  true  value 
are  due  to  purely  accidental  causes.  It  is  evident  that  the 
most  probable  value  of  the  true  measurement  is  typical  of  the 
whole  series,  and  that  the  degree  of  probability  of  any  devia- 


*  After  Thoma :  Untersuchungen  iiber  die  Grosse  der  anatomischea  Be- 
standtheile  des  menschlichen  Korpers  im  gesunden  und  kranken  Zastande. 
Leipzig,  1882.     Page  28. 


278 


Trans.  Acad.  iSci.  of  St.  Louis. 


tion  from  the  type  is  easily  calculated ;  for  example  in  the 
series  of -Table  No.  1,  the  chances  are  even  that  any  deviation 
will  fall  between  +1.0  cZ  and — 1.0  d,  for  it  has  been  seen  that 
half  the  whole  number  of  observations  fall  within  these  limits. 
Quetelet  demonstrated  that  the  method  of  grouping  related 
measurements  could  be  used  not  only  for  showing  the  most 
probable  height  of  one  individual  but  also  for  showing  the 
most  probable  or  typical  height,  i.  e.,  that  most  often  found,  of 
a  number  of  individuals.  The  Belgian  Astronomer  Koyal 
pointed  out  that  the  series  obtained  by  measuring  a  number 
of  individuals  of  the  same  type,  e.  g.,  men  of  the  same  nation- 
ality, was  characterized  by  the  peculiarities  that  distinguish 
a  series  in  which  the  deviations  from  the  typical  or  most 
probable  value  are  due  to  accidental  causes.  The  truth  of 
this  statement  is  obvious  when  the  two  are  compared. 


TABLE  No.  2.* 
Heights  of  United  States  Recruits. 


Height  at  Intervals  of 

One  Inch. 

Number  of  Recruits. 

Between  78  and  79  i 

nches 

2 

«'   77  ' 

'     78 

6 

i(   76  ' 

'  77 

9 

"   75  ' 

'  76 

42 

"        74  ' 

'  75 

118 

u        73  £ 

'     74 

343 

"   72  ' 

'  73 

680 

u        71  < 

'  72 

1485 

70  ' 

'  71 

2075 

"   69  ' 

'  70 

3133 

•'   68  ' 

'  69 

3631 

u        67  < 

'  68 

4054 

"   66  ' 

'  67 

3475 

"   65  ' 

'     66 

3019 

u   64  t 

'  65 

1947 

"        63  ' 

'    64 

1237 

"   62  * 

'     63 

526 

"   61  ' 

'     62 

50 

«'    60  ' 

'  61 

15 

59  ' 

'  60 

10 

"   58  ' 

'  59 

6 

"        57  ' 

•  58 

7 

56  « 

'  57 

3 

"   55  < 

'  56 

1 

"   55  ar 

id  less 

4 

Total...  25878 

*  E.  B.  Elliott's  table  in  Medical  Statistics  of  the  Provost- Marshal-Gen- 
eral's Bureau,  by  J.  H.  Baxter,  1875,  Vol.  I.     Introduction,  page  Ixxx. 


Porter —  The  Growth  of  St.  Louis  Children. 


279 


If  the  individual  heights  of  a  group  of  adults  are  found  to 
be  approximations  of  a  middle,  typical  height,  it  would  seem 
that  the  heights  of  children  of  the  same  sex,  age  and  class 
must  show  a  similar  relation  to  a  type ;  and  this  inference  is 
justified  by  observation. 


TABLE  No.  3. 
Observed  Distribution  of  the  Heights  of    2192    St. 

Girls,  Aged  8. 


Louis   School 


Heights  at  Intervals  of  2  Centimetres. 

Number  of  Observations. 

141  and  142  cm. 

1 

139 

140  '« 

137 

138  " 

1 

135 

136  " 

5 

133 

134  " 

10 

131 

132  <« 

2L 

129 

130  " 

28 

127 

128  " 

79 

125 

126  " 

138 

123 

124  " 

183 

121 

122  " 

243 

119 

120  " 

342 

117 

118  " 

321 

115 

116  «' 

297 

113 

114  " 

222 

111 

112  " 

137 

109 

110  " 

84 

107 

108  " 

42 

105 

106  " 

27 

103 

104  " 

8 

101 

102  " 

2 

99 

100  <' 

1 

- 

— 

Total 2192 


The  characteristics  of  a  series  in  which  the  individual  ob- 
servations are  accidental  deviations  from  a  typical  middle 
value  are  established  by  methods  which  have  long  been  used 
by  astronomers  and  mathematicians.  These  methods  seek  to 
determine  (1)  the  middle  or  typical  value  and  (2)  the  way  in 
which  the  individual  observations  are  dispersed  on  either  side 
of  this  value.  Some  statisticians  take  the  average  to  be  the 
nearest  approach  to  the  typical  value,  others  prefer  the  mean, 
i.  e.,  median  value.*  It  will  be  necessary  to  consider  at  some 
length  the  relative  value  of  average  and  mean  in  anthropomet- 
rical  studies  of  the  growth  of  children,  but  for  the  present  a 

*  Throughout  this  work  the  word  mean  is  used  as  the  synonym  of  median 
VALUE,  and  not  in  the  sense  of  arithmetical  mean,  which  is  called  here 
the  AVERAGE.  The  middle  value  will  be  employed  as  meaning  either 
Median  or  Average  value. 


280 


Trans.  Acad.  Sci.  of  St.  Louis. 


statement  of  the  methods  by  which  the  mean  and  average  are 
secured  will  suffice. 

By  AVERAGE  (A)  is  meant  the  quotient  obtained  by  divid- 
ins  the  sum  (2"  a)  of  the  values  (a)  obtained  in  the  individual 
measurements  by  the  whole  number  of  measurements  (?i). 


n 


(1) 


The  calculation  of  the  average  height  of  girls,  aged  9,  will 
serve  as  an  example. 

TABLE   No.  4. 

The  Calculation  of  the  Average  Height  of  St.  Louis  School 

Girls,  Aged  9. 


Heiglit  in 
Centi- 
metres. 

Number  of 
Observa- 
tions. 

Product. 

Height  in 
Centi- 
metres. 

Number  of 
Observa- 
tions. 

Product. 

168 

1 

168 

134 

25 

3350 

167 

133 

31 

4123 

166 

182 

29 

3828 

165 

131 

62 

8122 

164 

130 

78 

10140 

163 

129 

91 

11739 

162 

128 

119 

15232 

161 

127 

132 

16764 

160 

1 

160 

126 

143 

18018 

159 

125 

162 

20250 

158 

124 
123 

141 

17484 

157 

162 

19926 

156 

122 

145 

17690 

155 

121 

130 

15730 

154 

120 

145 

17400 

153 

119 

97 

11543 

152 

118 

94 

11092 

151 

117 

69 

8073 

150 

116 

59 

6844 

149 

115 

47 

5405 

148 

114 

30 

3420 

147 

113 

18 

2034 

146 

112 

11 

1232 

145 

111 

10 

1110 

144 

110 

10 

1100 

143 

1 

143 

109 

5 

545 

142 

2 

284 

108 

1 

108 

141 

3 

423 

107 

5 

535 

140 

2 

280 

106 

3 

318 

139 

3 

417 

105 

1 

105 

138 

9 

1242 

104 

1 

104 

137 

12 

1644 

103 

1 

103 

136 

15 

2040 

102 

135 

14 

1890 

101 

100 

2 

200 

Total 

71  =  2122 

r«=262358 

.        la       262358     ^^_, 

A  = =  =123.64  cm. 

n  2122 


Porter —  The  Growth  of  St.  Louis  Children.  281 

If  the  number  of  observations  is  very  large,  the  mean 
(MEDIAN  value,  M,)  may  be  found  with  considerable  accuracy 
by  a  mere  inspection  of  the  series.  The  mean  of  such  a 
series  is  the  measurement  which  most  frequently  recurs. 
Thus,  the  mean  height  of  the  recruits  of  Table  Xo.  2,  page  278, 
is  between  67  and  68  inches.  The  accuracy  with  which  the 
mean  can  thus  be  found  depends  not  only  on  the  number  of  ob- 
servations, but  also  on  the  size  of  the  units  of  measurement. 

For  most  purposes  it  is  desirable  to  know  not  merely  at 
which  inch,  centimetre,  kilogramme  or  other  unit  the  greatest 
number  of  observations  is  found,  but  exactly  at  what  fraction 
of  the  unit.  Again,  the  relation  between  the  number  of 
observations  and  the  size  of  the  unit  may  be  such  that 
the  largest  number  of  observations  at  one  unit  will  not 
fall  at  the  true  mean,  or  line  dividing  the  total  number 
of  observations  into  two  equal  groups.  The  method  by 
which  the  mean  can  be  calculated  with  exactness  will  be 
illustrated  by  the  following  example.  The  mean  height  of 
the  girls  in  Table  No.  4  is  obtained  by  adding  the  number 
of  observations  from  below  upwards  until  the  sum  cannot 
be'  increased  by  the  next  number  in  the  column  without 
exceeding  half  of  the  total  number  of  observations.  Thus 
1046  is  reached  opposite  123  cm. ;  the  next  number  in 
the  column  (141)  would  make  the  sum  1187,  which  is 
more  than  the  half  (1061)  of  the  total  number  of  observa- 
tions (2122).  The  mean  is,  therefore,  greater  than  123  cm. 
but  less  than  125  cm.  Its  position  is  found  by  interpolation. 
Half  of  the  total  number  of  observations  is  1061,  which  is  15 
more  than  the  sum  of  the  observations  up  to  124  cm.  ;  15  is 
11  per  cent,  of  141,  the  observations  at  124  cm.  Hence,  the 
mean  is  124.15  cm. 

Neither  the  mean  nor  the  average  can  give  any  information 
as  to  the  way  in  which  the  individual  observations  in  a  series 
are  distributed,  and  it  is  plain  that  two  series  having  an  iden- 
tical mean  or  average  may  differ  greatly  in  respect  of  the 
dispersion  of  the  individuals  from  the  middle  value.  Thus  the 
two  very  different  series  — 

4,  5,  6,  14,  15,  16 
9,  9,  10,  10,  11,  11 


282  Trans.  Acad.  Sci.  of  St.  Louis. 

have  the  same  average  (10).  The  best  measure  of  the  degree 
of  dispersion  or  deviation  of  the  individual  members  of  a  series 
from  their  common  mean  or  average  is  that  afforded  by  the 
Probable  Deviation.  The  probable  deviation  is  that  devia- 
tion from  the  middle  value,  which,  in  a  large  series  of  obser- 
vations, is  as  often  exceeded  as  attained  (Lexis).  In  other 
words,  half  of  the  whole  number  of  observations  fall  short 
of  the  probable  deviation,  while  the  other  half  exceed  it.  A 
deviation  which  exceeds  is  as  probable  as  one  that  does  not 
reach  thia  value.  The  probable  deviation  can  be  calculated 
with  the  formula  — 


d  =  ±  0.6745^^  -~-^  (2) 

In  this  formula: 

d  =  the  probable  deviation. 
Id^  =  the  sum  of   the  squares  of  the  individual  deviations 
from  the  mean  or  average. 
n  =  the  number  of  observations  in  the  series. 

In  the  place  of  this  formula,  in  which  the  calculation  of 
Sd'^  requires  much  labor  when  the  number  of  observations  is 
great,  a  simpler  formula  may  be  safely  used  in  getting  the 
deviation  in  a  large  series. 

d  =  ±  0.8453  —  (3) 

n 

The  formula  says  that  all  the  individual  deviations  from  the 
mean  or  average  of  a  series  must  be  added  together  without 
regard  to  whether  they  are  plus  or  minus  and  divided  by  the 
total  number  of  observations.  The  working  of  the  formula 
will  be  illustrated  by  finding  the  probable  deviation  from  the 
average  height  of  girls  aged  8. 


Porter  —  The  Growth  of  St.  Louis  Children. 


283 


TABLE  No.  5. 

The  Calculation  of  the  Probable  Deviation  (d)  from  the  Average 

Height  (118.36  Cm.)  of  2193  Girls,  aged  8. 


Height  at  Intervals  of 

V 

E  S 

2  Centimetres. 

0 

141  and  142  Cm. 

1 

23.64 

23.64 

139    "    140     " 

137    "    138     " 

1 

19.64 

19.64 

135    "    136     " 

5 

17.64 

88.20 

133    "    134     ♦' 

10 

15.64 

156.40 

181    "    132     " 

21 

13.64 

286.44 

129    "    130     '« 

28 

11.64 

325.92 

127    ''     128     " 

79 

9.64 

761.56 

125    «'    126     " 

188 

7.64 

1054.32 

123    "    124     '« 

183 

5.64 

1032.12 

121    "    122     «' 

243 

8.64 

884.62 

119    «'    120     " 

342 

1.64 

560.88 

117    "    118     " 

321 

0.36 

115.56 

115    "    116     " 

297 

2.36 

700.92 

113    "    114     " 

222 

4.36 

967.92 

111    "    112     " 

137 

6.36 

872.69 

109    "    110     " 

84 

8.36 

702.24 

107    "    108     " 

42 

10.36 

435.12 

105    "    106     " 

27 

12.36 

333  72 

103    "    104     " 

8 

14.36 

114.88 

101    "    102     " 

2 

16.36 

32.72 

99    "    100     «' 

1 

18.36 

18.36 

Total 

2192 

9487.77 

9487  77 
d  =  ±  0.8453     ^^^^    =  d=  3.698  Cm. 

The  distribution  of  the  above  series  of  the  heights  of  girls, 
aged  8,  is  therefore  characterized  by  a  probable  deviation  of 
±  3.7  cm.;  that  is,  one  against  one  may  be  wagered  that  no 
girl  aged  8  will  be  taller  than  122.06  cm.  or  shorter  than  114.66 
cm.     If  the  number  of  observations  falling  between  A  ziz  d, 

A  dr  2d,  A  zb  36? A  zh  "c?  be  noted,  a  complete  picture 

of  the  individual  observations  in  a  series  will  be  obtained. 
This  observed  distribution  may  then  be  compared  directly 
with  the  distribution  of  the  observations  in  an  hypothetical 
series  constructed  according  to  the  calculus  of  probabilities. 
The  observed  and  the  theoretical  series  should  correspond,  if 
the  causes  of  deviation  are  purely  accidental.  It  has  already 
been  said  that  such  a  comparison  must  be  made  before  it  can 
be  known  whether  the  observations  in  any  series  can  be 
treated  by  the  methods  of  the  theory  of  probabilities.  It  is 
however  not  necessary  to  compare  more  than  one  of  a  num- 


284 


Trans.  Acad.  Set.  of  St.  Louis. 


ber  of  series  in  which  the  distribution  follows  a  common 
type.  It  will  suffice  for  our  purposes  therefore  to  compare 
the  distribution  of  the  2192  heights  in  Table  No.  3,  page  279, 
with  the  distribution  of  an  equal  number  according  to  the 
calculus  of  probabilities.  The  method  by  which  this  is  done 
permits  the  construction  of  a  curve  from  the  observations 
actually  made  which  shall  be  the  probable  form  of  a  curve 
representing  the  distribution  of  the  entire  class  from  which 
the  observations  have  been  drawn. 

The  number  of  observation  (Z)  which  should  be  included 
between  the  average  (A)  and  any  deviation  from  the  average, 
in  other  words  any  multiple  {m)  of  the  probable  deviation 
(cZ),  is  obtained  from  the  equation.* 

t 

viri 

The  labor  of  calculating  deviations  with  the  aid  of  this 
equation  is  avoided  by  the  use  of  such  tables  as  Stieda's, 
reproduced  below. 


-t2 


dt 


(4) 


TABLE   No.  6. 

Stieda's  Table  for  Calculating  the  Number  of  Observations  at  any 
Distance  from  the  Mean  or  Average  within  the  Limits:  M-j- 
5d  AND  M  — 5d. 


p 

Percent. 

P 

Percent. 

0.1 

5.4 

1.8 

77.5 

0.2 

10.7 

1.9 

80.0 

0.3 

16.0 

2.0 

82.3 

0.4 

21.3 

2.1 

84.3 

0.5 

26.4 

2.2 

86.2 

0.6 

31.4 

2.3 

87.9 

0.7 

36.3 

2.4 

89.5 

0.8 

41.1 

2.5 

90.8 

0.9 

45.6 

2.6 

92.1 

1.0 

50.0 

2.7 

93.1 

l.I 

54.2 

2.8 

94.1 

1.2 

58.2 

2.9 

95.0 

1.3 

61.9 

3.0 

95.7 

1.4 

65.5 

3.5 

98.2 

1.5 

68.8 

4.0 

99.3 

1.6 

71.9 

4.5 

99.8 

1.7 

74.8 

5.0 

99.93 

*  Kramp.  L'Analyse  des  refractions  astronomiques. 


Porter  —  The  Growth  of  St.  Louis  Children.  285 

If  p  is  allowed  to  represent  one  of  the  figures  in  the  first 
column  and  A  the  average  of  all  the  measurements  in  a  series, 
the  figures  opposite  p  in  the  second  column  will  give  the  per 
cent,  of  individual  measurements  lying  within  the  limits  : 

K  -\-  p  .  d  and  A  —  p  .  d 

Suppose  for  example  it  were  required  to  know  how  many 
of  a  series  of  2192  girls  aged  8  were  of  a  height  between  the 
average  (118.36  cm.)  and  a  deviation  of  ±  l-'5  d  (1.5.  3,7 
cm.  =  5.55  cm.),  i.  e.  between  118.36  cm.  +  5.55  cm.  = 
123.91  cm.  and  118.36  cm.  —  5.55  cm.  =  112.81  cm. 
The  number  in  the  table  opposite  1.5  is  68.8,  which 
says  that  68.8  per  cent,  of  the  2192,  or  1508,  should  fall 
within  the  limits  stated.  Then  half  this  number  must  fall 
between  A  and  A  +  1.5  cZ  (118.36  cm.  and  123.91  cm.).  In 
a  similar  manner  it  will  be  found  that  50  per  cent,  of  the 
whole  number,  or  1096,  should  fall  within  the  limits  Aid 
(118.36  cm.  +  3.7  cm.  =  122.06  cm.  and  118.36  cm.  —  3.7 
cm.  =  116.51  cm.),  and  25  per  cent,  between  A  and  K  -\-  d 
(118.36  cm.  and  122.06  cm.).  Thus  may  be  calculated  the 
number  of  observations  which  should  occur  at  any  deviation 
from  the  average.  The  theoretical  and  observed  distribution 
of  2192  girls,  aged  8,  is  compared  in  Table  No.  7. 


286 


Trans.  Acad.  Sci.  of  St.  Louis. 


TABLE   No.  7. 

The  Theoretical  and  the   Observed  Distribution  of  the  Heights 
OF  2192  Girls,  Aged  8. 


Probable 
Deviation 

d. 

Heights  at  Intervals  of 

Theoretical 

Observed 

of  zb  0.5d. 

Distribution, 

Distribution. 

+  5,0  d 

136.86  Cm, 

2 

2 

+  4.5'^ 

135.01    " 

6 

8 

+  4.0  " 

133.26    " 

12 

18 

4-3.5  " 

131.31    " 

27 

27 

+  3.0'' 

129.46    " 

54 

57 

+  2.5" 

127.61    " 

93 

104 

+  2.0'^ 

125.76    " 

148 

150 

+  1.5  " 

123.91     " 

206 

209 

+  1.0  " 

122.06     " 

259 

286 

+  0.5  " 

120.21     " 

289 

300 

0.0  « 

118.36     " 

—  0.5" 

116.51    " 

289 

272 

—  1.0  " 

114.66    " 

259 

275 

—  1.5" 

112.81    '* 

206 

196 

—  2.0  " 

110,96    " 

148 

126 

—  2.5  " 

109.11    " 

93 

80 

—  3.0  " 

107.26    " 

54 

40 

—  3.5  •• 

105.41    " 

27 

26 

—  4.0  «' 

103.56    " 

12 

12 

—  4.5  " 

101,71    '• 

6 

3 

—  5,0  '« 

99,86    " 

Total 

2 

2 

2192 

2192 

The  curves  in  Plate  I  *  give  a  graphic  representation  of  the 
figures  in  Table  No.  7.  A  glance  at  these  curves  shows  that 
there  is  a  close  agreement  between  them,  indicating  that  the 
individual  observations  out  of  which  they  are  constructed  are 
symmetrically  grouped  about  a  middle  value  typical  of  the 
whole,  and  proving  that  the  material  with  which  we  have  to 
deal  satisfies  the  requirements  of  theory. 

The  method  of  showing  distribution  just  described  is  not 
the  only  method  used  for  this  purpose.  Francis  Gallon  f 
determines  the  actual  distribution  of  the  observations  in  a 
series  at  intervals  of  5  or  10  per  cent,  from  the  median  or 
50  '*  percentile  grade."  The  calculation  of  the  median  value 
(mean)  or  50  percentile  grade  has  already  been  described: 
that  for  the  5,  10,  20  and  other  percentile  grades  is  similar  in 


*  The  plates  are  placed  after  the  index  at  the  end  of  the  number. 
t  Natural  Inheritance.     London,  1889. 


Porter  —  The  Grotvth  of  St.  Louis  Children. 


287 


principle.     The  percentile    grades    of   the   heights  of   girls, 
aged  9,  are  as  follows:  — 

TABLE  No.  8. 
The  Percentile  Distribution  of  the  Heights  of  Girls,  Aged  9. 


Percentile  Grades. 

Number  of 
Observations. 

Heights. 

95 

2015.9 

133.42  Cm. 

90 

1909.8 

130.97 

80 

1697.6 

128.62 

75 

1591.5 

127.58 

70 

1485.4 

126.54 

60 

1273.2 

125.53 

50 

1061.0 

124.11 

40 

848.8 

122.76 

30 

636.6 

121.21 

25 

530.5 

120.90 

20 

424.4 

119.59 

10 

212.2 

117.12 

5 

106.1 

115.17 

Total 

2122 

The  Probable  Error  of  the  Average  can  be  determined  by 
means  of  the  formula 

E:=±         =  (5)* 

V    n 

whe~reE  =  the  probable  error  of  the  average, 

d  =  the  probable  deviation  of   an  individual  from   the 

average, 
n  =  the  number  of  observations  in  the  series. 


Substituting  the  values  determined  for  the  heights  of  girls, 
aged  9,  we  have  — 

3.698 
E  =  dz  =jz  0.079  cm. 

V  2122 
The  values  of  E  are  siven  in  Table  No.  9. 


*  Formulas  (1),  (2),  (3)  and  (5)  and  Table  No.  6  are  taken  from  L. 
Stieda's  admirable  article  :  Ueber  die  Anwendung  der  Wahrscheinlichkeits- 
rechnung  in  der  anthropologischen  Statistik.  Archiv.  fiir  Anthropologic, 
Bd.  xiv.,  1882,  p.  167-182. 


288 


Trans.  Acad.  Sci.  of  St.  Louis. 


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Porter  —  The  Growth  of  St.  Louis  Children.  289 

The  mean  or  average  of  the  observations  at  any  age  in  the 
period  of  growth  is  typical  of  the  child  at  that  age,  and  a  com- 
parison of  the  means  at  different  ages  will  reveal  the  law  of 
growth  of  the  type.  Again,  the  mean  of  the  observations  at  any 
deviation  from  the  mean  of  the  whole  number,  for  example 
the  height  at  a  deviation  oi  -\-  d  from  the  mean,  or,  if  Galton's 
method  is  employed,  the  height  at  any  percentile  grade,  is  the 
type  of  those  who  stand  at  a  certain  degree  of  deviation  from 
the  type  of  the  whole  number.  Thus  types  of  tall  and  short, 
light  and  heavy  children  are  secured.  The  types  of  the  same 
degree  of  deviation  from  the  mean  at  all  ages  are  as  compar- 
able as  the  type  of  the  whole  number  of  observations,  and 
reveal  the  growth  of  the  typically  tall  and  short,  light  and 
heavy  children ;  but  the  comparison  is  less  secure  the  greater 
the  deviation  from  the  mean,  for  the  probable  error  is 
inversely  as  the  square  of  the  number  of  observations,  and 
the  number  of  observations  rapidly  diminishes  on  either  side 
of  the  mean. 

The  methods  described  in  this  chapter  have  been  employed 
in  the  present  investigation.  For  every  entire  series  here 
presented,  the  mean  and  the  average,  the  probable  deviation 
and  the  probable  error,  and  the  5,  10,  20,  25,  30,  40,  50,  60, 
70,  75,  80,  90  and  95  percentile  grades  have  been  calcu- 
lated. The  25  and  75  percentile  grades  were  obtained  by 
dividing  by  2  the  sums  of  the  20  and  80,  and  the  70  and  80 
percentile  grades  respectively. 


CHAPTER    III. 

TRUSTWORTHINESS    OF    THE   MATERIAL;    ITS    LIMITATIONS.      COMPARISON    OP 
MEDIAN   AND   AVERAGE   VALUES. 

The  question  first  to  be  decided  in  the  discussion  of  an 
anlhropometrical  series  is  whether  the  individual  observations 
are  so  related  one  to  another  that  they  constitute  accidental 
deviations  from  a  middle  value.  The  method  of  answering 
this  question  by  comparing  the  series  of  observations  with  a 
series  constructed  according  to  the  theory  of  probabilities  has 
already  been  described,  and  it  has  been  stated  incidentally  that 
the  heights  of  St.  Louis  girls  aged  8  agreed  with  the  theoretical 
series  in  their  distribution.  Where  such  an  agreement  exists, 
the  individual  observations  are  to  be  regarded  as  approxima- 
tions of  a  middle  value  which  is  the  type  of  the  series.  It  is 
not  necessary  to  make  this  comparison  at  more  than  one  age, 
or  in  more  than  one  dimension,  for  it  is  known  that  if  one 
series  in  a  group  like  that  with  which  we  have  to  deal  shows 
this  agreement  the  other  series  will  be  found  to  do  the  same. 
In  the  present  case,  additional  evidence  of  the  correspondence 
between  observation  and  theory  could  be  furnished,  were  it 
required,  by  Table  No.  10,  containing  the  probable  deviation 
(290) 


Porter  —  The  Growth  of  St.  Louis  Children. 


291 


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292  Trans.  Acad.  Sci.  of  St.  Louis. 

from  the  average.  It  is  seen  in  this  table  that  the  probable 
deviations  are  small,  that  is,  one-half  of  the  observations 
deviate  but  little  from  the  middle  value,  which  is  one  of  the 
fundamental  attributes  of  deviations  due  to  accidental  causes. 
But  additional  evidence  is  hardly  required,  and  few  critics  will 
object  to  regarding  the  middle  values  in  this  investigation  as 
types  of  their  respective  series. 

The  objection  sometimes  made  that  the  errors  of  observation 
materially  affect  the  truth  of  the  values  obtained  is  of  little 
weight,  partly  because  such  errors  are  "  accidental  "  and  com- 
pensate each  other  as  already  explained,  and  partly  because  a 
deviation  from  the  middle  value  due  to  an  uncompensated 
error  in  measurement  forms,  as  a  rule,  an  inconsiderable  part 
of  that  greater  deviation  which  expresses  the  physiological 
difference  between  the  individual  and  the  type  of  his  age  and 
class.  Accidental  errors  of  observation  need  not  give  concern 
in  measurements  of  great  numbers  of  school  children.  Nor 
need  there  be  much  fear  of  constant  errors  of  observation, 
provided  the  collection  of  material  is  made  by  many  persons 
and  with  a  good  number  of  each  sort  of  measuring  instrument. 
If  hundreds  of  teachers  take  part  in  the  measurements,  as  in 
the  present  investigation,  a  constant  cause  of  error  due  to  a 
teacher's  unconscious  bias  or  personal  equation  on  one  side  of 
the  middle  value  will  very  probably  be  compensated  by  the 
bias  of  another  teacher  on  the  opposite  side,  and,  similarly, 
if  a  number  of  scales  are  used,  the  errors  of  those  which  weigh 
too  lightly  are  likely  to  be  compensated  by  the  errors  of  those 
whose  readings  are  too  heavy. 

The  trustworthiness  of  this  material  must  be  encouraging  to 
those  whose  hold  on  the  theory  underlying  these  matters  is 
not  very  strong,  because  it  illustrates  the  truth  that  the  types 
of  physical  development,  and  the  laws  of  growth  of  the  type 
may  be  induced  from  measurements  made  by  comparatively 
unskilled  hands  and  demonstrates  that  a  system  of  anthropo- 
metrical  measurements  may  be  fruitfully  employed  in  the 
public  schools. 

The  use  to  which  middle  values  and  the  deviations  from 
middle  values  shall  be  put  is  in  part  the  subject  of  controversy, 
and  it  will  be  well  to  state  here  the  manner  in  which  they 


Porter  —  The  Groicth  of  St.  Louis  Children.  293 

shall  be  employed  in  the  present  work.  In  doing  so  it  will  be 
necessary  to  give  a  brief  account  of  the  matters  concerning 
which  agreement  is  general  as  well  as  those  which  are  in  dispute. 

It  is  acknowledged  generally  that  the  method  of  Quetelet 
furnishes  a  middle  value  typical  of  the  series  from  which 
it  was  drawn,  for  example  the  middle  weight  of  boys  of 
the  same  age,  nationality  and  social  condition  is  the  typical 
weight  of  boys  of  that  age  and  class;  and  it  is  further 
acknowledged  that  the  increase  in  the  middle  value  from  year 
to  year  expresses  the  law  of  growth  of  the  type.  It  follows 
that  the  middle  value  of  those  who  stand  at  any  deviation  from 
the  middle  value  of  the  whole  number  is  the  type  of  that 
degree  of  deviation  from  the  type  of  the  whole  number  and 
that  the  increase  in  the  middle  value  at  the  same  degree  of 
deviation  at  each  age  in  the  period  of  growth  expresses  the  law 
of  growth  of  the  type  at  that  degree  of  deviation.  Thus  the 
curves  of  percentile  grades  printed  below  express  the  growth 
of  the  typical  St.  Louis  school-boy  and  girl.  The  type  at  a 
certain  deviation  from  the  mean  of  an  age  will  show  the  same 
degree  of  deviation  from  the  mean  at  any  subsequent  age; 
for  example  a  type-boy  in  the  75  percentile  grade  at  age  6 
will  throughout  his  growth  be  heavier  than  75  per  cent,  of 
boys  of  his  own  age.  Percentile  curves  are  of  course  not 
necessarily  parallel.  The  type  of  the  50  per  cent,  who  exceed 
the  middle  value  of  the  whole  number  has  a  law  of  growth 
characteristic  of  tall  boys  and  different  from  that  of  the  type 
of  the  50  per  cent,  who  fall  below  the  middle  value  of  the 
whole  number. 

The  application  of  the  middle  value  to  individuals  has  not 
yet  been  mentioned.  It  is  here  that  controversy  finds  its 
hold.  The  relation  of  the  individual  to  the  type  is  not  known. 
It  is  not  known  whether  a  boy  who  at  age  6  is  heavier  than 
75  per  cent,  of  boys  at  his  age  will  at  age  18  be  heavier  than 
75  per  cent,  of  boys  at  that  age.  Some  anthropologists 
believe  that  there  is  at  least  probability  that  children  remain 
in  the  same  percentile  grade  throughout  life,  while  others 
dissent  from  this  view.  In  truth  the  development  of  the 
individual  has  been  little  studied,  and  it  is  therefore  not  yet 
possible  to  state  his  probable  future  growth. 


294  Trans.  Acad.  Sci.  of  St.  Louis. 

This  question  — the  relation  of  the  "growth  of  the  individual 
to  the  growth  of  the  type  —  can  be  determined  only  by  the 
individualizing  method.  The  generalizing  method  deals  solely 
with  units,  irrespective  of  their  individuality.  If  for  example 
John  Smith  in  the  75  percentile  grade  and  William  Harrison 
in  the  60  percentile  grade  at  age  6  exchange  places  at  age  7, 
the  personal  curve  of  each  boy  undergoes  an  important  devia- 
tion, but  the  number  of  units  in  the  two  grades,  and  conse- 
quently the  middle  value  in  each,  is  unaltered.  The  generalizing 
method,  therefore,  furnishes  no  data  by  which  the  future  de- 
velopment of  individuals  can  be  safely  judged.  The  individ- 
ualizing method,  on  the  contrary,  follows  the  individual  from 
year  to  year  throughout  his  growth  and  establishes  the 
frequency  and  extent  of  his  deviations  from  the  growth  of 
the  type.  The  lack  of  data  collected  by  the  individualizing 
method  is  regrettable,  but  this  gap  in  our  knowledge  does  not 
prevent  the  establishing  of  physical  standards  by  which  the 
probability  that  the  physique  of  any  child  is  normal  or  abnor- 
mal can  be  fixed. 

The  facts  stated  above  limit  the  application  of  middle  values 
to  (1)  the  establishing  of  physical  standards  at  each  age,  and 
(2)  the  using  of  these  standards  to  determine  whether  the 
physique  of  any  child  is  normal:  they  do  not,  in  the  present 
state  of  knowledge,  permit  prediction  of  future  growth. 

It  has  been  much  disputed  whether  the  median  value  or  the 
average  should  be  taken  for  the  type.  Many  investigators 
agree  with  Sir  John  Herschel,  who  declares  in  his  celebrated 
review  of  Quetelet's  Lettres  sur  la  theorie  des  probabilites 
(page  23)  that  an  average  "  may  be  convenient,  to  convey  a 
"  ofeneral  notion  of  the  things  averaged,  but  involves  no  con- 
"  ception  of  a  natural  and  recognizable  central  magnitude  all 
"  differences  from  which  ought  to  be  regarded  as  deviations 
"from  a  standard.  The  notion  of  a  mean,  on  the  other 
"  hand,  does  imply  such  a  conception,  standing  distinguished 
"from  an  average  by  this  very  feature,  viz.:  the  regular 
"  march  of  the  groups,  increasing  to  a  maximum,  and  thence 
"  again  diminishing.  An  average  gives  us  no  assurance  that 
"  the  future  will  be  like  the  past.  A  mean  may  be  reckoned 
*'  on    with   the    most    implicit    confidence.      All    the    phil- 


Porter  —  The  Growth  of  St.  Louis  Children.  295 

'*  osophical  value  of  statistical  results  depends  on  a  due 
*'  appreciation  of  this  distinction  and  acceptance  of  its 
*<  consequences." 

Other  statisticians  have  used  the  average  exclusively.  Out 
of  respect  to  this  difference  of  opinion,  both  the  median  value 
and  the  average  have  been  employed  in  the  present  work. 
On  calculating  these  values  for  each  series,  it  was  found  that 
the  difference  between  them  was  inconsiderable,  showing  that 


296 


Trans.  Acad.  ScL  of  St.  Louis. 


TABLE   No.  11. 
Median  Minus  Average  Values. 


Dimensions. 

Sex. 

Unit  of 
Measure- 
ment. 

Age  at  Nearest  Birthday,  and  Median  Minus  Average  Values. 

6 

7 

8 

9 

10 

11 

12 

Weight 

Boys. 

Girls. 

Kilogramme 

+0.10 

+0.06 

-0.01 

—0.01 

+0.09 

—0.03 

+0.16 

—0.04 

+0.04 

—0.04 

+0.08 
—0.35 

—0.10 

—0.41 

Height  Standing 

Boys. 

Girls. 

Centimetre.. 

+0.29 

+0.43 

-0.54 

+0.66 

+0.45 

+0.49 

+0.64 

+0.38 

+0.52 

+0.44 

+0.68 

+0.42 

+0.60 

+0.41 

+0.36 

+0.43 

Height  Sitting 

Boys. 

Girls. 

Boys. 

Girls. 

Centimetre.. 

—0.10 

+0.64 

+0.47 

+0.99 

+0.35 

+0.03 

-0.40 

+0.69 

+0.42 

+0.59 

+0.13 

+0.55 

Span  of  Arms 

Centimetre.. 

+0.62 

+0.33 

+0.66 

+0.75 

+0.66 

—0.20 

+0.49 

+0.65 

+0.39 

+0.43 

+0.46 

+0.22 

—0.12 

+0.53 

Girth  of  Chest, 

Inspiration. 

Boys. 

Girls. 

Centimetre.. 

+0.20 

+0.58 

+0.30 

+0.28 

+0.17 

+0.57 

+0.49 

+0.56 

+0.44 

+0.49 

+0.47 
+0.55 

+0.40 

+0.48 

+0.41 

+0.19 

Girth  of  Chest, 

Expiration. 

Boys. 

Girls. 

Boys. 

Girls. 

Centimetre. . 

+0,34 

+0.48 

+0.24 

+0.51 

+0.56 

+0.48 

+0.37 

+0.48 

+0.22 

+0.40 

+0.40 

+0.12 

Strength  of  Squeeze, 
Right  Hand 

Kilogramme 

+0.21 

+0.79 

—0.02 

+0.03 

+0.21 

+0.13 

-0.70 

—0.09 

-0.19 

—  0.18 

-0.11 

-0.06 

-0.08 

+0.27 

-0.14 

—0.07 

Strength  of  Squeeze, 
Left  Hand 

Boys. 

Girls. 

Kilogramme 

+0.53 

+0.69 

—0.04 

+0.54 

—0.02 

—0.22 

-0.13 

—  0.59 

—0.23 

+0.02 

—0.29 

+0.05 

Length  of  Head 

Boys. 

Girls. 

Millimetre.. 

+0.47 

+0.89 

+0.38 
+0.49 

+0.82 
+  1.23 

+0.28 
+  1.41 

+0.06 

+1.28 

+0.49 

+1.67 

+0.24 

+1.07 

Width  of  Head 

Boys. 

Girls. ' 

Millimetre.. 

+0.47 
+0.56 

+0.61 

+0.70 

+0.33 

+0.53 

+0.21 

+0.54 

+0.52 

+0.79 

+0.31 

+0.49 

+0.38 

+0.67 

Root  of  Nose  to 

Point  of  Chin. 

Boys. 

Girls. 

Millimetre.. 

-0.52 

—0.53 

-0.30 

—0.57 

-0.20 

—0.05 

-0.09 

—0.25 

-0.33 

—0.37 

-0.14 

—0.24 

+0.20 

+0.07 

Width  of  Eace 

Boys. 

Girls. 

Millimetre.. 

+0.96 

+0.68 

+0.62 

+0.27 

+0.93 

-0.18 

+0.84 
+0.79 

+0.03 

+0.93 

+0.49 

+0.47 

+0.78 
+0.63 

Point  of  Chin. 

Boys. 

Girls. 

Millimetre.. 

+0.34 

+0.39 

+0.76 

+0.83 

+0.54 

+0.41 

+0.82 
+0.32 

+0.33 

+0.52 

+0.72 
+0.85 

+0.39 

+0.66 

Porter  —  Tlie  Groioth  of  St.  Louis  Children. 


29' 


TABLE   No,  11  —  Continued. 
Median  Minus  Average  Values. 


Age  at  Nearest  Birthday,  and  Median  Minus  Average  Values. 

13 

14 

15 

16 

17 

18 

19 

20 

21 

Dimensions, 

-0.36 

—0.49 

—0.46 

+0.36 

—0.73 

+0.16 

+0.35 

+0.78 

-0.07 

+0.78 

+0.23 

—0.29 

—0.36 

—0.09 

+0.74 

+0.09 

+0.08 

+0.28 

—0.34 

Weight. 

+0.38 

—0.34 

+0.28 
+1.10 

+1.00 

+0.51 

+0.87 
+0.07 

+1.10 

+0.42 
+0.69 

+0.52 
+0.74 

Height  Standing, 

+0.29 

+0.49 

-0.13 

+0.93 

+0.94 

+0.74 

+0.94 

+0.75 

-0,53 

+0.69 

+0.82 

Height  Sitting, 

+0.24 

+0.64 

+0.34 

+0.98 

+0.36 

—0.17 

+1.35 

+0.80 

+1.02 

+0.61 

+0.90 

+0.41 

+0.19 

+0.91 

+0.45 

+1.33 

—0.39 
—0.64 

Span  of  Arms. 

+0.39 

+0.30 

+0.23 

+0.43 

+0.24 

+0.12 

+0.52 

+0.17 

-0.52 

+0.31 

+1.01 

+0.57 

+1.23 

+0.48 

+0.90 

+0.80 

Girth  of  Chest, 

Inspiration. 

+0.41 

+0.40 

+0.08 

+0.48 

+0.35 

+0.16 

+0.72 
+0.26 

+0.44 

+0.45 

+0.51 

+0.41 

+0.61 

Girth  of  Chest, 

Expiration. 

-0.09 

—0.62 

-0.50 

—0.24 

—1.14 

—0.18 

+0.37 

+0.75 

+0.02 

—0.16 

+0.44 

+0.43 
+0.38 

-0.11 

Strength  of  Squeeze, 
Right  Hand. 

—0.36 

—  0,12 

-0.50 

—0.69 

+0.08 

+0.41 

+0.54 

—0.08 

+0.60 

—0,10 

+0.48 

—0.28 

Strength  of  Squeeze, 
Left  Hand. 

+0.37 

+1.04 

-0.69 

+1.30 

+0.68 
+0.55 

+0.98 
+0.86 

+1.48 
+0,46 

+0.40 

+0.27 

Length  of  Head. 

+0.27 
^0.37 

+0.54 

+0.35 

+0.78 
+0.42 

+0.37 

+0.72 

+0.41 

+0.39 

+0.34 

+1.07 

+1.06 
—0.38 

—0.12 
+0.04 

Width  of  Head. 

+0.10 

-0.21 

+0.08 
—0.15 

-0.11 

—0.39 

+0.10 

—0.61 

+0.55 

+0.71 

—0.26 

+0.53 

+0.94 

+0,46 

+1.79 

+0.75 

+0.16 

+0.27 

—0.06 

Root  of  Nose  to 

Point  of  Chin, 

+0.19 

+0.71 

+0.51 

+0.84 

+0.71 

+0.45 

+0.75 

+0..55 

+0.20 

+1.29 

Width  of  Face. 

+0.54 

+0.80 

+0.55 

+0.62 

+0.78 
+0.65 

-0.03 

+0.90 

+1.99 

+0.96 

1 
—1.831     —0,09 

+1.78 

Hair  Line  to 

Point  of  Chin. 

298  Trans.  Acad.  Sci.  of  St.  Louis. 

either  may  be  used  for  the  type  without  any  error  of  prac- 
tical importance,  provided  the  series  are  similar  to  those 
analyzed  here.  This  point  is  of  practical  interest  because 
the  labor  of  reckoning  the  average  is  much  greater  than  in 
reckoning  the  median  value. 

Bowditch,  in   The   Growth  of  Ghildren,  Boston,   1891,  p. 
495  e<  seq.,  discusses  the  relation  of  median  and  average  value. 
"It  is  evident,"  he  writes,  "  that  the  value  M  will  tend  to 
"  approximate  to  the  average  value  of  all  the  observations  and 
*'  will  be  identical  with  it   when  the  [percentile]  curve  S  T 
*'is  symmetrically  disposed  on  both  sides  of  M,  i.  e.,  when 
"  the  values  at  sixty,  seventy,  eighty,  ninety  and  ninety-five 
"per  cent,  exceed  M  by  the  same  amount,  respectively,  by 
"  which  the  values  at  forty,  thirty,  twenty,  ten  and  five  per 
"  cent,  fall  short  of  it.     If  A  represent  the  average  value  of 
"  all  the  observations,  then  the  value  of  M-A  will  be  a  meas- 
"  ure  of  the  direction   and  extent  of  the  asymmetry  of  the 
"  curve  S  T,for  this  value  will  be  zero  when  the  curve  is  sym- 
^^  metrical i  positive  v^hen   the  values  at  the  lower  percentile 
"  grades  fall  short  of  M  more  than  those  at  the  higher  grades 
"  exceed  it,  and  negative  when  the  reverse  is  the  case.''     [Dr. 
Bowditch  now  gives  a  table  of  median  minus  average  height 
and  weight.]     "  An  examination  of  this  table  or  of  the  curves 
"  constructed  from  it,   as  given  in  Plate  I,  shows   that   the 
"  asymmetry  of    the  curves    of  percentile  grades  varies  very 
"  much,  at  different  ages,  both  in  direction  and  amount.     The 
"  variation  in  the  value  of  M-A  in  the  curves  of  height  is  much 
"  the  same  as  that  in  the  curves  of  weight  for  each  sex  consid- 
"  ered  by  itself,  but  there  is  a  great  difference  between  the 
"  two    sexes.     This    difference    shows    itself  most    distinctly 
"between  the  ages  of  eleven  and  fifteen  years.     During  this 
"  time  a  rise  in  the  curves  for  the  males  coincides  with  a  fall 
"  in  those  for  the  females,  while  before  and  after  this  period 
"  the  curves,  as  a  rule,  rise  and  fall  together.     We  must  con- 
"  elude,  therefore,   that  the  rate  of  annual  increase,  both  in 
"  height  and  weight,  is  different  at  different  percentile  grades, 
"  or,  in  other  words,  that  large  children  grow  differently  from 
"  small  ones,  and  moreover,  that  between  the  ages  of  eleven 
"  and  fifteen  years  there  is  a  striking  difference  in  the  mode 
"  of  growth  of  the  two  sexes." 


Porter  —  The  Growth  of  St.  Louis  Children.  299 

Table  No.  11  and  the  curves  constructed  from  it  (Plates  II, 
III,  IV)  furnish  considerable  material  for  the  study  of  the 
relation  between  median  and  average  values.  The  curves  of 
median  minus  average  heia^ht  aojree  with  those  of  Dr.  Bow- 
ditch  in  showing  (1)  a  difference  in  the  rate  of  growth  of  the 
same  sex  at  different  percentile  grades,  (2)  an  agreement  in  the 
rate  of  growth  of  the  sexes  from  age  6  to  12,  inclusive,* 
and  (3)  a  marked  difference  in  the  rate  of  growth  from  age  12 
to  age  16,  beyond  which  the  number  of  observations  is  per- 
haps too  small  for  sure  work.  In  the  curves  from  both  cities, 
moreover,  the  greatest  asymmetry  in  girls  is  near  age  13,  and 
in  boys  near  age  16,  the  culmination  being  a  little  later  in  St. 
Louis  children,  and  the  least  asymmetry  is  near  age  12. 
The  asymmetry  of  Boston  bo3'.s'  curves  at  age  15  and  girls' 
curves  at  ages  16  and  17  is  somewhat  greater  than  that  of  the 
St.  Louis  curves.  It  is  further  worthy  of  notice  that  the 
values  in  the  case  of  St.  Louis  boys  do  not  become  negative. 

There  is  a  general  similarity  also  between  the  median  minus 
average  weights  of  the  children  of  the  two  cities,  the  asym- 
metry of  girls  being  again  greatest  about  age  14  and  of  boys 
greatest  at  about  age  16.  Dr.  Bowditch's  conclusions,  quoted 
above,  are  therefore  fully  confirmed. 

The  St.  Louis  curves  on  Plates  II,  III  and  IV  should  now 
be  compared  with  each  other.  The  maximum  asymmetry  of 
girls  about  14  years  and  boys  about  16  years  old,  appears  in 
weight,  height,  height  sitting,  and  span  of  arms,  while  the 
remaining  curves  exhibit  no  characteristic  sexual  differences 
during  the  period  of  prepubertal  acceleration.  The  asym- 
metry is  for  the  most  part  positive,  weight,  strength  of 
squeeze  and  height  of  face  from  root  of  nose  to  point  of  chin 
being  the  only  considerable  exceptions.  Sexual  differences, 
aside  from  those  already  mentioned,  are  unimportant,  save 
perhaps  in  length  and  width  of  head,  in  both  of  which  the 
asymmetry  of  girls  is  greater  than  that  of  boys  from  age  6  to 
age  13, 

The  errors  in  the  median  minus  average  values  of  height, 
weight  and  other  single  dimensions  may  be  partially  compen- 


*  It  should  be  remembered  that  Dr.  Bowditch's  ages  are  recorded  at  last 
birthday,  while  mine  are  recorded  at  nearest  birthday. 


300 


Trans.  Acad.  Sci.  of  St.  Louis. 


sated  by  adding  the  median  minus  average  values  of  several 
dimensions  of  each  sex  and  age,  without  regard  to  plus  or 
minus  sian.     This  has  been  done  in  Table  No.  12. 


TABLE   No.  12. 
Sums  of  Median  minus  Average  Values. 


J  at  Nearest 
Birthday. 

Weight,  Height 

Standing,  Height 

Sitting,  Span  of 

Arras. 

Girth  of  Chest  at 
Full  Inspiration 
and  Expiration. 

Strength  of 
Squeeze,  Right 
and  Left  Hand. 

Head  and 

Face 
Measure- 
ments. 

M 
< 

Boys, 

Girls. 

Boys. 

Girls. 

Boys. 

Girls. 

Boys. 

Girls. 

6 

1.55 

1.48 

0.54 

1.06 

0.74 

1.48 

2.76 

3.05 

7 

1.22 

1.89 

0.54 

0.79 

0.06 

0.57 

2.67 

2.86 

8 

1.86 

1.60 

0.73 

1.05 

0.23 

0.35 

2.82 

2.40 

9 

1.52 

1.16 

0.86 

1.04 

0.89 

0.27 

2.24 

3.31 

10 

1.51 

1.58 

0.66 

0.89 

0.24 

0.65 

1.27 

3.89 

11 

1.56 

1.57 

0.87 

1.03 

0.31 

0.29 

2.15 

3.72 

12 

0.71 

1.92 

0.81 

0.31 

0.43 

0.12 

1.99 

3.10. 

13 

1.27 

1.96 

0.80 

0.70 

0.45 

0.74 

1.47 

3.13 

14 

1.21 

3.37 

0.31 

0.91 

1.00 

0.93 

2.37 

3.26 

16 

1.51 

1.89 

0.76 

0.29 

0.60 

0.72 

3.06 

2.46 

16 

3.52 

2.34 

1.36 

0.73 

1.68 

0.26 

2.26 

3.43 

17 

3.19 

1.52 

1.62 

0.67 

0.47 

4.65 

2.96 

18 



2.42 

1.77 

0.93 



0.77 

3.40 

3.29 

The  conclusions  drawn  from  the  curves  discussed  above  are 
substantiated  in  the  main  by  this  table.  It  is,  however,  dif- 
ficult to  believe  that  a  sexual  difference  such  as  exists  in 
weight,  height  standing,  height  sitting  and  span  of  arms 
will  not  be  found  also  in  girth  of  chest  and  the  various 
dimensions  of  the  head.  But  a  purely  objective  attitude 
towards  the  material  in  hand  does  not  permit  speculation  as 
to  what  might  be  revealed  if  the  material  were  very  much 
larger  and  its  intrinsic  laws  easier  to  unveil. 


CHAPTER   IV. 

DANGERS  OF  COMPARING   MEASUREMENTS  OF  CHILDREN  IN   DIFFERENT    COUN- 
TRIES.     INFLUENCE  OF  OCCUPATION  AND  NATIONALITY  OF    PARENTS. 

It  has  been  a  custom  of  anthropometrists  to  compare  the 
type-children  of  cities,  states  or  provinces  very  different  in 
situation  and  character.  Such  comparisons  may  be  expected 
always  to  show  that  the  laws  of  growth  are  in  their  main 
features  the  same  for  all  children.  They  cannot,  however,  be 
expected  to  give  very  definite  information  in  regard  to  the 
relative  size  of  children  of  different  countries  or  districts 
so  long  as  the  social  status  or  environment  of  the  children 
is  not  more  closely  studied.  The  children  in  the  public 
schools  are  from  all  classes  of  society,  and  it  has  been 
demonstrated  repeatedly  that  the  favored  classes  differ 
physically  from  the  poor.  The  children  of  the  prosperous 
have  been  found  to  be  larger  than  the  children  of  the  poor. 
The  comparison  of  middle  values  got  from  two  sets  of  schools 
is  therefore  open  to  the  objection  that  the  composition  of  the 
school  population  may  not  be  the  same  in  both  sets.  It  would 
for  example  be  unsafe  to  say  that  St.  Louis  children  are 
larger  or  smaller  than  Copenhagen  children  because  the  type- 
children  in  the  St.  Louis  Public  Schools  are  larger  or  smaller 
than  the  type-children  in  Copenhagen,  for  the  difference 
observed  may  depend  on  the  different  composition  of  the 
school  population  in  the  two  cities. 

Such  comparisons,  when  rightly  made,  are  not  only  of 
great  scientific  interest  but  are  almost  essential  to  the  use 
of  anthropometrical  systems  in  education.  An  immense 
saving  of  time  would  be  made  if  it  were  shown  that  the 
typical  height,  weight,  etc.,  of  children  in  one  city  of  a 
country  could  be  adopted  as  the  standard  for  the  schools  of 
the  entire  country  or  even  a  considerable  part  of  it.  And  in 
any  one  city,  the  application  of  the  type-values  to  individuals 
would  be  much  less  liable  to  error  if  it  were  known  how  much 
allowance  should  be  made  for  the  difference  between  the  type 

(301) 


302 


Trans.  Acad.  ScL  of  St.  Louis. 


of  a  special  social  class  and  the  types  of  a  mixed  school  pop- 
ulation. Every  investigation  of  the  present  kind  should, 
therefore,  include  information  concerning  the  social  condition 
of  the  children.  The  tax-returns  .are  available  for  this  pur- 
pose, and  the  occupation  of  parents  is  also  of  use.  It  was 
not  possible  to  inquire  into  tax-returns  in  the  present  re- 
search, but  some  facts  can  be  communicated  regarding  the 
physical  differences  between  the  children  of  professional  and 
business  men  and  those  of  manual  tradesmen.  The  occupa- 
tions included  under  these  heads  may  be  seen  in  the  following 
statement  of  the  occupations  of  the  fathers  of  2,000  St.  Louis 
children.  The  names  of  occupations  are  set  down  as  given 
by  the  pupils. 


PROFESSIONS. 


Artist. 


3      Minister. 


Chemist 1 

Civil  Engineer 8 

Dentist i 

Editor 6 

Electrical  Engineer i 

Electrician 2 

Lawyer 14 


Medical  Student 1 

Musician 6 

Photographer 3 

Physician 13 

Teacher 9 

Veterinarian 1 


Total 76 


MERCANTILE  CLASS. 


Agent 36 

Banker 2 

Book-keeper 40 

Broker 9 

Cashier 8 

Clerk 3 

Collector 8 

Contractor 20 

Dairyman 8 

Drugs 10 

Dealer  in  Butter 1 

Carpets 2 

Cattle 4 

Cloth 4 

Clothes 1 

Corn 2 

Coal 4 

Feed  and  Flour 2 

Fish  and  Oysters 3 

Fruits 3 


Dealer  in  Furniture 6 

Hardware 2 

Hats ...  1 

Horses 1 

Lime 1 

Lumber 4 

Marble 1 

Pork 2 

Produce 2 

Stationery 1 

Stone 1 

Tobacco 5 

Wall-paper 1 

Foreman 24 

Grocer 36 

Hotel-keeper 5 

Inspector,  Building 2 

Street 7 

Not  specified 1 

Jeweler 7 


Porter  —  The  Growth  of  St.  Louis  Children. 


303 


Insurance ...  4 

Manager 7 

Manufacturer 35 

Merchant 143 

Merchant  Tailor 2 

News-depot 1 

Optician 2 

Postmaster 1 


President  of  Iron  Co 1 

Publisher 1 

Keal  Estate 7 

Salesman 76 

Secretary  of  a  corporation 6 

Telegrapher 1 

Traveling  Salesman 9 

Undertaker 3 


Total 579 


MANUAL  TRADES. 


Baker 24 

Barber ,  23 

Blacksmith 29 

Book-Binder 2 

Brewer 14 

Bricklayer 21 

Builder 9 

Butcher 40 

Carpenter 148 

Carriage  Eepairer 2 

Cigar  Packer 1 

Cloth  Sponger 1 

Compositor 2 

Confectioner 7 

Cook 5 

Cooper 37 

Coppersmith 1 

Cord-Wainer 1 

Dairyman 1 

Decorator 4 

Draughtsman 5 

Dressmaker 4 

Dyer 2 

Engineer 43 

Engraver 1 

Fireman 11 

Eoundryman 2 

Gardener 5 

Gilder 1 

Glass  Blower 2 

Iron  Worker 3 

Laundryman 1 

Lithographer 1 

Locksmith 1 

Maker  of : 

Bags 2 

Baskets 1 

Belts 1 


Maker  of : 

Boilers 7 

Boxes 9 

Brushes 3 

Candies 3 

Carriages  16 

Chains 2 

Chairs 2 

Cigars 31 

Collars 1 

Cornices .  1 

Harness 2 

Lanterns 1 

Mattresses 1 

Models 1 

Organs 1 

Patterns 4 

Shoes 47 

Tobacco 3 

Trunks ...  I 

Wagons 6 

Watches 6 

Machinist 55 

Maltster 4 

Marble  Cutter 3 

Mechanic 42 

Miller 7 

Millwright 5 

Miner 1 

Molder 33 

Motorman 2 

Packer 5 

Painter 51 

Paper-Hanger 8 

Paver 4 

Pipe-Fitter 2 

Planer 1 

Plasterer 10 


304 


Trans.  Acad.  Sci.  of  St.  Louis. 


Plumber 13 

Polisher 1 

Potter 2 

Printer 19 

Puddler 1 

Saddler 12 

Selector  of  Tobacco 1 

Shoe  Varnisher 1 

Slater 1 

Stair  Builder 4 

Stone  Mason 50 


Tailor 56 

Tanner 6 

Tinner  15 

Turner 6 

Upholsterer 5 

Varnisher 5 

Waterproofer  and  Painter 1 

Weaver 1 

Whitener U 

Wood- Worker 33 


Total 1086 


LABORERS. 


Baggageman 2 

Carriers,  Letter 9 

Carriers,  Paper 6 

Coal-heaver 1 

Driver 3 

Elevator  man 1 

Engine-cleaner 1 

Expressman 3 

Eireman 11 

Gripman 6 

Hostler 7 

Huckster 2 

Janitor 3 

Laborer 31 

Live-stock  driver 1 

Lumberman .- 1 

Mill-hand 4 


Oiler 2 

Peddler 19 

Policeman  and  watchman 21 

Porter 4 

Riverman 1 

Railway-hand 12 

Saloon-keeper 51 

Sexton 1 

Shepherd 1 

Steward,  Hotel 2 

'*        Steamer 1 

"         3 

Teamster 6 

Waiter 1 

Total 216 


MISCELLANEOUS. 


Captain  of  Steamer. 

Conductor 

Farmer.. 

"Independent ". . .. 

Pilot c. 

No  occupation  

"Retired" 


Total. 


1 
14 
12 
1 
5 
7 
3 

43 


SUMMARY. 

Professions 76 

Mercantile  classes 579 

Manual  trades 1086 

Laborers 216 

Miscellaneous 43 


Total 2000 


Porter  —  The  Grotvih  of  St.  Louis  Children. 


305 


The  number  of  children  of  rich  families  and  of  very  poor 
families  in  the  public  schools  is  small,  the  larger  part  of  the 
pupils  being  from  what  would  be  called  in  England  the  lower 
middle  class,  and  the  school  population  is  accordingly  more 
homogeneous  than  would  have  seemed  possible  at  the  first 
glance. 

The  difference  in  the  weight  of  children  of  the  professional 
and  merchant  class  is  probably  of  little  importance  until  the 
period  of  prepubertal  acceleration.  Such  at  least  is  the 
inference  from  Table  No.  13,  where  the  weights  of  these  two 
classes  are  compared. 

TABLE  No.  13. 

A.  Comparison  of  the  Weights  of  the  Daughters  of  Manual  Trades- 
men WITH  THE  Weights  of  the  Daughters  of  Professional  Men 
AND  Merchants. 


Professional  Men  and  Merchants. 

Manual  Tradesmen. 

Age   at 
Nearest 

Number  of 
Observa- 

Median 
Weight. 
(Kilo- 
grammes) 

Median 
Weight. 
(Kilo- 
grammes) 

Number  of 
Observa- 

Age at 

Nearest 

Birthday. 

tions. 

tions. 

Birthday. 

6 

74 

19.53 

18.95 

237 

6 

7 

148 

20.63 

20.74 

604 

7 

8 

170 

23.00 

22.89 

723 

8 

9 

152 

25.48 

25.09 

688 

9 

10 

168 

27.61 

27.46 

651 

10 

11 

173 

30.63 

29.45 

569 

11 

12 

153 

33.86 

32.28 

556 

12 

13 

160 

39.04 

37.07 

402 

13 

14 

140 

43.59 

41.68 

251 

14 

15 

112 

47.49 

45.62 

145 

15 

16 

87 

50.16 

49.18 

52 

16 

17 

46 

53.58 

51.07 

24 

17 

What  is  true  of  weight  is  in  this  instance  probably  true  of 
the  physical  development  as  a  whole,  and  Table  No.  13  would 
seem  to  indicate  that  a  wide  difference  in  social  status  or 
material  prosperity  may  exist  without  much  influencing  the 
growth  of  children  up  to  the  prepubertal  acceleration.  But 
further  investigation  is  necessary  before  a  generalization  can 
be  made.  It  must  suffice  here  to  state:  1.  The  daughters  of 
professional  men  and  merchants  are  very  little  heavier  than 
the  daughters  of  manual   tradesmen   until  the  period  of  pre- 


806  Trans.  Acad.  Sci.  of  St.  Louis. 

pubertal  acceleration.  2.  The  weight  of  girls  is  much  more 
influenced  by  the  material  prosperity  or  social  status  of 
parents  during  and  immediately  after  the  period  of  pre- 
pubertal acceleration  than  in  the  earlier  years  of  growth. 

The  proportion  of  children  of  the  more  prosperous  class  in 
the  public  schools  is  not  the  same  in  all  grades.  In  the  higher 
grades,  containing  the  older  children,  the  number  from  pros- 
perous families  is  relatively  larger,  the  children  of  the  poor 
having  in  many  instances  been  compelled  to  leave  school  in 
order  to  earn  money.  Some  idea  of  the  extent  of  this  change 
may  be  gained  from  Table  No.  14,  in  which  the  per  cent,  of 
daughters  of  professional  men  and  merchants  and  daughters 
of  manual  tradesmen  is  given  at  each  age  and  school  grade. 


Porter  —  The  Growth  of  St.  Louis  Children. 


307 


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308 


Trans.  Acad.  Sci.  of  St.  Louis. 


The  ratio  betw^een  the  two  is  more  easily  grasped  when  the 
difference  between  the  classes  at  each  age  and  grade  is  stated, 
black  type  being  used  where  the  professional  and  merchant 
class  exceed  the  tradesmen's  daughters  and  lower  case  type 
where  the  contrary  is  true. 


Age. 

Kinder- 
garten. 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

% 

VIII. 

6 

7 

3.9% 
6.1 

0.0 

3.9% 

6.8 
15.9 
13.7 

4.0 

1.6 
0.3 

% 
0.7 
15.7 
2.2 

13.0 
3.5 
3.9 
0.8 

% 

% 

% 

% 

% 

a 

0.6 
7.4 
1.1 

17.1 
5.7 
8.1 
1.1 
0.3 

9 

2.2 
15.0 
17.0 

3.0 
8.4 
9.1 
5.6 
1.5 

in 

0.7 
3.6 
6.9 
6.4 

7.4 
3.7 
5.6 

0.3 
0.1 
3.2 
4.1 
3.4 
3.5 
4.9 

11 

12 
13 

0.6 
1.7 
4.4 
1.5 
5.9 

5.6 

14 

11.2 

15 

11.8 

16 

4.0 

The  number  of  boys  withdrawn  from  school  to  earn  money 
is  of  course  greater  than  the  number  of  girls  withdrawn. 
Thus  of  562  boys,  aged  6,  17.8  per  cent,  were  sons  of  pro- 
fessional men  or  merchants  and  42.9  per  cent,  sons  of  manual 
tradesmen,  while  at  age  14,  29.3  per  cent,  of  498  boys  were 
from  the  former  class  and  37  per  cent,  from  the  latter. 


Age 
at  Nearest 
Birthday. 

Number    of 
Individuals. 

Sons  of  Pro- 
fessional Men 
and  Merchants. 

Sons  of 

Manual 

Tradesmen. 

Others. 

6 
14 

562 
498 

17.8% 
29.3 

42.9% 
37.0 

39.3% 
33.7 

The  nationality  of  the  children  should  be  considered  in  an 
anthropometrical  inquiry.  It  is  well  known  that  children  of 
the  same  age  but  different  nationality  exhibit  differences  in 
physical  development.  The  annual  report  of  the  Superinten- 
dent of  Public  Schools,  issued  Aug.  1,  1891,  contains  in  Table 
V,  appendix,  page  XL VI,  a  statement  "  Showing  the  Birth- 
place of  Pupils  Eegistered  in  Each  School  for  the  Year 
1890-91,"  from  which  the  number  of  pupils  in  the  schools  in 
which  the  measurements  were  made  has  been  taken  and  the 
following  percentages  calculated :  — 


Porter  —  The  Groivtli  of  St.  Louis  Children. 


309 


BIRTHPXACB    OF   46,870  PUPILS  IN   THE   ST.   LOUIS   PUBLIC   SCHOOLS. 

St.  Louis 79.26  % 

other  Parts  of  the  United  States 16.92  " 

Great  Britain 0.63  " 

Ireland 0.19  " 

German  States 1.97  " 

Other  Foreign  Countries 0.87  " 

Unknown 0.16  '* 

Total 100 

The  children  of  foreign  birth  are  too  few  to  affect  the 
results  of  the  measurements,  and  the  number  of  children  born 
in  or  near  St.  Louis  is  such  that  the  middle  values  obtained 
must  be  taken  as  characteristic  for  this  community. 

The  children  of  foreign  parentage  are  of  course  much  more 
numerous  than  those  of  foreign  birth.  The  number  of  Ger- 
mans is  especially  large.  The  median  weights  of  boys  and 
girls  whose  parents  were  born  in  Germany  are  compared  in 
Tables  No.  15  and  16,  with  children  of  American  parentage. 


TABLE  No.  15.* 
The  Weights  of  Girls  whose  Parents  were  born  in  Germany  com- 
pared WITH  the  Weights  of  Girls  whose  Parents  were  born  in 
the  United  States.! 


*  The  birth-place  of  the  girls  themselves  is  not  considered  in  this  table. 
t  A  few  were  born  in  Canada. 


310 


Trans.  Acad.  Sci.  of  St.  Louis. 


TABLE   No.  16.* 

■The  Weights  of  Boys  whose  Parents  were  born  in  Germany  Com- 
pared WITH  THE  Weights  of  Boys  whose  Parents  were  born  in 
THE  United  States. f 


GERMAN. 

AMERICAN. 

Age  at 

Nearest 

Birthday. 

Number  of 
Observa- 
tions. 

Median 
Weight. 
(Kilo- 
grammes) 

Median 
Weight. 
(Kilo- 
grammes) 

Number  of 
Observa- 
tions. 

Age  at 

Nearest 

Birthday. 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

158 
334 
426 
369 
370 
358 
385 
321 
166 
106 
26 

20.04 
21.93 
23.98 
26.64 
28.51 
31.21 
33.51 
35.92 
39.59 
44.68 
52.22 

19.66 
21.67 
23.91 
26.08 
28.49 
31.26 
33.45 
35.96 
40.34 
47.25 
52.10 
55.14 

263 
756 
907 
878 
847 
668 
549 
437 
352 
219 
92 
40 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

The  difference  in  weight  is  seen  to  be  of  no  great  impor- 
tance. 

In  the  absence  of  special  investigations  of  the  influence  of 
social  condition  and  the  nationality  of  parents  on  the  growth 
of  children,  it  is  impossible  to  estimate  accurately  to  what 
degree  middle  values,  calculated  without  regard  to  social  con- 
dition and  nationality,  are  affected  by  these  factors.  The 
data  presented  in  this  chapter  go  to  show  that  the  middle 
values  of  St.  Louis  children  are  little  influenced  by  ponsider- 
able  differences  in  social  condition  before  the  period  of 
prepubertal  acceleration  and  are  not  very  largely  influenced 
by  such  differences  during  this  period.  Further,  these  values 
are  at  no  time  much  affected  by  differences  in  nationality  of 
parents  not  greater  than  those  existing  between  Germans  and 
Americans.  But  the  whole  question  evidently  requires  ex- 
tended study  of  data  difficult  or  impossible  of  collection  by 
private  hands. 


*  The  birth-place  of  the  boys  themselves  is  not  considered  in  this  table, 
t  A  few  were  born  in  Canada. 


CHAPTER    V. 

PERCENTILE  GRADES  OF  WEIGHT,  HEIGHT  STANDING,  HEIGHT  SITTING,  SPAN 
OF  ARMS,  GIRTH  OF  CHEST,  LENGTH  OF  HEAD,  WIDTH  OF  HEAD,  HEIGHT  OF 
FACE  FROM  ROOT  OF  NOSE  TO  POINT  OF  CHIN,  WIDTH  OF  FACE,  AND  HEIGHT 
OF  FACE  FROM  HAIR  LINE   TO  POINT  OF  CHIN. 

The  Percentile  Grades  of  weight,  height,  etc.,  presented  in 
Tables  No.  17  to  No.  28,  inclusive,  are  represented  graphically 
in  Plates  V  to  XXIV.  By  their  aid,  the  percentile  rank  of 
an  individual  in  respect  of  weight,  span  of  arms  or  any  physi- 
cal dimension  included  in  the  tables  can  be  easily  and  quickly 
determined.  Suppose,  for  example,  the  percentile  rank  of  a 
boy,  aged  11,  weighing  32  kg.  was  desired.  A  horizontal  line 
is  drawn  from  32  in  the  column  of  kilogrammes  on  the  left  of 
Plate  V  to  the  curve  of  age  11,  and  a  perpendicular  is  dropped 
from  the  point  of  intersection  to  the  scale  of  percentile 
grades  at  the  bottom  of  the  plate.  The  perpendicular  falls  at 
60  per  cent.  Hence  the  boy  is  heavier  than  60  per  cent,  of 
boys  of  his  age  and  lighter  than  40  per  cent. 

Other  facts  are  made  plain  by  these  curves.  The  increase 
at  any  percentile  grade  during  one  or  more  years  is  expressed 
by  the  distance  between  the  curves  at  that  grade.  Thus,  in 
Plate  V,  the  gain  in  weight  of  the  type-boy  in  the  15  per- 
centile grade  during  the  years  6  to  11  inclusive  is  9.3  kg.,  and 
the  gain  at  the  85  percentile  grade  during  the  same  year  13.0 
kg.  The  difference  in  size  between  large  and  small  boys  of 
the  same  age  appears  in  the  inclination  of  the  curve  to  its 
axis,  the  slope  being  steepest  in  the  years  of  quickest  growth. 
And  finally,  the  tendency  of  the  greater  number  of  individuals 
to  approximate  the  middle  value  of  their  group  is  illustrated, 
the  inclination  of  each  curve  being  much  less  at  the  central 
part  than  at  the  ends,  where  the  giants  and  the  dwarfs  are 
found.  The  principal  service  of  such  curves,  however,  is  to 
determine  percentile  rank. 

(311) 


312 


Trans.  Acad.  Sci.  of  St.  Louis. 


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CHAPTER  VI. 


SEXUAL  DIFFERENCES  IX    GROWTH. 


When  the  curves  of  growth  in  weight,  height  standing, 
height  sitting,  span  of  arms  and  girth  of  chest  are  drawn  on 
the  same  system  of  co-ordinates,  as  has  been  done  in  Plates 
XXV  to  XXIX  inclusive,  the  attention  of  the  observer  is 
arrested  by  the  extraordinary  difference  in  the  development 
of  girls  and  boys  during  the  period  of  prepubertal 
acceleration.  Girls  enter  this  time  of  rapid  growth  at  age  11 
or  12,  two  years  earlier  than  boys,  and  during  several  years  are 
larger  than  boys  of  the  same  age.  The  period  during  which 
girls  are  larger  than  boys  does  not  correspond  exactly  with 
the  period  of  accelerated  development,  but  begins  and  ends 
a  little  later.  The  ages  at  which  girls  begin  and  cease  to  be 
larger  than  boys  are  given  in  the  following  table.     The  ages 

TABLE  No.  29. 
Ages  at  which  Girls  begin  and  cease  to  be  larger  than  Boys. 


DIMENSION. 


Weight 

Height  standing 

Height  sitting 

Span  of  arms 

Girth  of  chest 

Height  of  face  from 
hair  line  to  point  of 
chin 


Age  at  which  Girls  begin 
to  be  larger  than  Boys. 


Percentile  Grades. 


12i\-yrs. 
HA 

12A 


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Age  at  which  Girls  cease 
to  be  larger  than  Boys. 


Percentile  Grades. 


26 


IGAyrs, 
l5fo    " 
16H   " 
ISA    " 
16-A-   " 


50 

15/j-yrs. 

ISA 

(( 

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it 

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are  nearly  the  same  for  the  same  percentile  grade  in  all  five 
dimensions.     An   examination    of  plates   XXX    to    XXXVI 

(324) 


Porter  —  The  Growth  of  St.  Louis  Children. 


325 


shows  that  the  sexual  difference  just  noted  is  not  present  in 
expansion  of  chest,  or  in  strength  of  squeeze,  or  in 
any  head  or  face  measurement  except  height  of  face  from 
hair-line  to  point  of  chin.  Boys  have  therefore  a  larger  ex- 
pansion of  the  chest,  greater  strength  of  squeeze  and  greater 
leno;th  and  width  of  head  and  height  and  width  of  face  than 
girls  throughout  their  period  of  growth. 

An  interesting  comparison  can  be  made  of  the  duration  of 
the  period  in  which  girls  are    larger  than  boys.     It  appears 

Duration  of  the  Period  during  which  Girls  are  larger  than  Boys. 


DIMENSION. 


Weight 

Height  standing 
Height  sitting... 
Span  of  arms  . . . 
Girth  of  chest... 


Percentile  Grades. 


3i%yrs. 

4  " 

5  " 

3A     " 


3-1%  yrs. 

Qli       <( 
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5         " 

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75 


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3-3-      '< 
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Q   5  (( 

<5i2 


that  the  period  is  shortest  in  span  of  arms  and  is  considerably 
longer  in  height  sitting  than  in  any  other  dimension. 

The  age  at  which  girls  begin  to  be  larger  than  boys  differs 
at  different  percentile  grades,  big  girls  (75  percentile  grades) 
beginning  to  be  larger  than  big  boys  at  an  earlier  age  than 
that  at  which  small  girls  begin  to  exceed  small  boys.  A 
difference  is  seen  also  in  the  duration  of  the  period  in  which 
girls  are  larger  than  boys:  the  small  girls  keep  their 
superiority  during  a  longer  time  than  the  larger  girls. 

Sexual  differences  are  further  displayed  in  Plates  XXXVII 
to  XLI,  inclusive,  in  which  the  percentile  curves  of  both  sexes 
are  drawn  one  a  short  distance  under  the  other,  and  the  points 
at  which  girls  begin  and  cease  to  be  heavier  than  boys  joined 
by  heavy  unbroken  lines.  The  early  superiority  of  large 
girls  and  the  relative  early  loss  of  their  superiority  is  seen  in 
all  the  plates.  The  fact  that  the  period  during  which  big  girls 
are  larger  than  big  boys  is  shorter  than  the  period  during  which 


326  Trans.  Acad.  Set.  of  St.  Louis. 

little  girls  are  larger  than  little  boys  is  very  clearly  demon- 
strated by  Plates  XXXVIII,  Height  Standing,  XXXIX, 
Height  Sitting  and  XL,  Span  of  Arms  ;  it  can  be  seen  also 
in  Plate  XXXVII,  Weight,  and  XLI,  Girth  of  Chest,  if  the 
ninety  and  the  five  percentile  grades,  in  which  the  small 
number  of  observations  has  probably  led  to  error,  are 
neglected. 


CHAPTER    VII. 


THE   RATE   OP   GROWTH. 


The  Absolute  Annual  Increase  is  the  gain  in  weight  or  height, 
etc.,  during  the  twelve  preceding  months  ;  thus,  the  absolute 
annual  increase  in  height  at  age  7  is  the  gain  in  weight  during 
the  twelve  months  from  age  6  to  age  7,  obtained  by  subtract- 
ing the  average  or  median  weight  at  age  6  from  that  at  age  7. 

The  absolute  annual  increase  of  height  standing,  weight  and 
span  of  arms  is  shown  in  Plate  XLII  and  Tables  No.  30,  31 
and  32.  In  all  three,  the  maximum  for  girls  is  at  age  13  and 
the  maximum  for  boys  at  age  15.  The  same  may  be  said  of 
the  curves  for  height  sitting,  girth  of  chest  and  strength  of 
squeeze,  in  Plate  XLIII,  from  Tables  No.  33,  34,  44  and  45, 
although  the  curves  are  less  regular,  owing  to  the  observations 
being  more  difficult  than  those  from  which  the  preceding  plate 
was  constructed.  In  all  six  curves,  the  small  number  of  ob- 
servations at  age  17  and  18  cause  the  median  values  at  those 
ages  to  be  less  reliable  than  at  other  ages. 

The  Relative  Annual  Increase  is  the  increase  for  any  year 
divided  by  the  average  value  at  that  year  ;  thus,  the  relative 
annual  increase  in  weight  at  age  7  is  the  difference  between 
the  average  weight  at  age  6  and  age  7  divided  by  the  average 
weight  at  age  6.  The  relative  annual  increase  gives  a  truer 
idea  of  growth  than  the  absolute  annual  increase,  because  the 
latter  value  is  entangled  with  the  size  of  the  individual  meas- 
ured. The  absolute  increase  is  commonly  greater  in  a  big 
boy  than  in  a  small  boy,  and  yet  the  rate  of  growth  may  be 
the  same.     The  relative  annual  increase  is  free  of  such  errors. 

The  relative  annual  increase  in  strength  of  squeeze,  weight, 
height  standing,  height  sitting,  span  of  arms  and  girth  of 
chest  is  drawn  in  Plate  XLIV.  The  gain  in  weisrht  during  the 
prepubertal  acceleration  is  extraordinary  in  both  girls  and 
boys,  as  is  the  rapid  fall  immediately  thereafter.  The  quick- 
ness of  growth  in  height  standing  of  boys  is  slightly  greater 

(327) 


828 


Trans.  Acad.  Sd.  of  St.  Louis. 


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Porter —  The  Groivth  of  St.  Louis  Children.  333 

during  the  years  6  and  7  than  at  any  other  time,  and  in 
girls  is  nearly  as  great  in  these  years  as  in  the  period  of 
acceleration.  The  curve  of  girls'  height  sitting  is  very  similar 
to  that  of  girls'  height  standing.  In  both,  the  rate  of  growth 
is  more  uniform  than  in  weight.  Indeed,  the  period  of  accel- 
eration in  the  last  named  dimension  is  greater  than  in  any  of 
the  others.  The  relative  annual  increase  of  boys'  height  sit- 
ting seems  almost  atypical,  by  reason  of  its  sharp  ascent 
at  ages  8  and  9  and  its  failure  to  sink  after  age  16. 
The  latter  feature  is  perhaps  due  to  an  error  in  the  average 
value  caused  by  the    small  number  of  observations    at    age 

17.  I  am  unable  to  explain  the  ascent  at  ages  9  and 
10.  The  growth  in  span  of  arms  is  somewhat  more  rapid 
at  ages  7  and  8  than  during  the  prepubertal  acceleration. 
The  curve  of  girls'  girth  of  chest  differs  from  the  usual 
type  in  its  sudden  rise  at  age  11,  the  increase  at  that  year 
appearing  slightly  greater  than  at  age  13.  The  boys' 
curve,  on  the  contrary,  agrees  very  well  with  the  curves  of 
weight,    height,    etc.,    except   that    the    curve    rises    at    age 

18,  where  the  number  of  observations,  it  may  be  repeated, 
is  perhaps  too  small  for  very  sure  work.  The  quickness 
with  which  the  strength  of  squeeze  decreases  after  age  7 
is  certainly  remarkable,  as  is  the  sharpness  with  which  the 
prepubertal  acceleration  is  shown. 

Attention  will  be  called  in  chapter  IX,  to  the  importance 
in  children  of  the  relation  between  height  and  weight,  girth  of 
chest  and  other  physical  dimensions.  Unusual  height,  it  will 
be  pointed  out,  is  commonly  a  disadvantage,  because  it  entails 
an  unusual  loss  of  energy.  If  such  individuals  have  a  weight 
and  girth  of  chest,  etc.,  so  much  above  the  common  as  to  com- 
pensate their  excessive  height,  they  are  likely  to  be  able  to 
meet  all  demands  on  their  strength.  If  they  do  not  possess 
this  compensatory  development,  they  will  probably  be  unable 
to  meet  any  excessive  demand.  Thus  the  question  of  how  far 
this,  compensation  exists  in  any  individual,  or,  more  broadly 
stated,  the  question  what  weight,  girth  of  chest,  etc.,  should 
accompany  any  given  height,  becomes  of  the  greatest  in- 
terest. This  interest,  it  should  be  remarked,  is  unusually 
great  in  the  case  of  children,  for  children  are  taxed  with  the 


334  Trans.  Acad.  Sci.  of  St.  Louis. 

mechanical  motion  and  other  forms  of  dissipation  of  energy 
making  up  the  ordinary  output  of  life,  and,  in  addition,  with 
the  extraordinary  function  of  storing  energy  in  the  increase 
of  tissue  which  constitutes  growth. 

In  view  of  these  facts,  Plate  XLV  cannot  fail  to  be  instruct- 
ive. It  shows  the  ratio  of  span  of  arms,  height  sitting,  chest- 
girth,  weight,  strength  of  squeeze  with  right  hand,  and  five  head 
and  face  measurements  to  height  standing.  Height  standing 
is  here  expressed  by  an  abscissa,  and  the  percentage  relation 
of  weight  and  the  other  dimensions  are  displayed  in  curves. 
Of  all  these,  span  of  arms  most  closely  approximates  the 
height,  the  difference  being  less  than  one  per  cent,  of  the 
latter  from  age  6  to  11  and  scarcely  more  than  2  })er  cent, 
in  subsequent  ages.  Span  of  arms  in  both  sexes  is  therefore 
nearly  the  same  as  height  standing  throughout  the  period  of 
observation,  becoming  very  slightly  greater  than  the  height  as 
growth  progresses.  The  height  sitting  and  the  girth  of  chest 
run  a  parallel  course  and  are,  moreover,  nearly  equal,  the 
girth  of  chest  being  about  2  per  cent,  less  than  the  height 
sitting.  They  increase  a  little  less  rapidly  than  the  height, 
showing  a  decline  of  about  4  per  cent,  in  thirteen  years. 
Height  sitting  and  chest-girth  are  not  far  from  half  the  height 
standing. 

Far  different  is  the  development  of  weight  and  strength  of 
squeeze.  These  increase  much  more  rapidly  than  height,  for 
at  age  6  the  height  stands  to  weight  in  the  ratio  of  100  to  18 
and  to  strength  of  squeeze  as  100  to  6,  while  at  age  16  these 
ratios  are  100  to  34  and  100  to  about  16,  respectively.  The 
parallelism  in  the  development  of  weight  and  strength  of 
squeeze  is  of  much  interest.  The  dimensions  of  head  and 
face  increase  somewhat  less  rapidly  than  the  height.  The 
length  of  head,  for  example,  falls  from  -rg-th  of  the  height,  at 
age  6,  to  about  iVth  at  age  18. 


CHAPTER    VIII. 

THE       RELATION       BETWEEN       THE     PHYSICAL     DEVELOPMENT       OF      SCHOOL 
CHILDREN   AND    THEIR   CAPACITY    FOR    MENTAL   LABOR. 

Ill  Vol.  VI,  No.  7  of  the  Transactions  of  the  Academy  of 
Science  of  St.  Louis,  issued  March  21,  1893,  I  demonstrated 
that  children  who  possess  more  than  the  ordinary  power  of 
mental  labor,  as  measured  by  their  progress  in  their  studies, 
are  heavier,  taller  and  larger  in  girth  of  chest  and  in  width  of 
head  than  their  less  gifted  companions  of  the  same  age.  A 
more  extended  statement  of  these  observations  was  presented 
to  the  Berliner  Gesellschaft  fiir  Anthropologic,  Ethnologic 
und  Urgeschichte,  July  15,  1893,  and  appears  in  Virchow's 
Zeitschrift  fiir  Ethnologic  under  the  title  Untersuchungen  der 
Schulkinder  in  Bezug  auf  die  physischen  Grundlagen  ihrer 
geistigen  Entwickelung.  In  these  papers,  the  material  was 
the  total  number  of  observations  irrespective  of  the  social 
condition  of  parents.  An  example,  selected  from  Tables  Nos. 
2  and  4,  page  165  and  167,  of  The  Physical  Basis  of  Pre- 
cocity and  Dullness,  will  illustrate  the  result  of  the 
inquiry.  Pupils  aged  11  are  found  in  Grades  I,  II,  III,  IV, 
V  and  VI  of  the  St.  Louis  Public  Schools,  as  the  following 
table    shows.     The    59  boys  of    Grade  I,  the    lowest   grade, 

TABLE   No.  35. 

Median  Weight  of  Boys  aged  U   distributed  by  School  Grade. 

No.  of  Boys  Median 

Grades.  Weighed.  Weight. 

1 59  28.83  Kg. 

II 311  29.74 

III 664  30.92 

IV 546  31.43 

V 123  32,41 

VI 33  33,29 

weigh  less  than  the  boys  of  Grade  II,  and  these,    again,  are 
lighter  than  the  boys  in  higher  grades. 

(335) 


336  Trans.  Acad.  Sci.  of  St.  Louis. 

It  is  a  well-known  fact  that  children  of  the  prosperous 
classes  are  better  developed  physically  than  the  children  of 
the  poor.  It  has  been  suggested  that  the  children  of  poor 
parents  are  not  so  successful  in  school  work  as  the  children 
of  the  rich,  and  that  the  poor  children  are  compelled  to  leave 
school  at  an  earlier  age  than  the  rich,  and  for  these  reasons 
are  relatively  less  numerous  than  the  rich  in  the  higher  grades. 
According  to  this  idea,  the  better  physical  development  of 
the  children  of  the  same  age  in  the  higher  grades,  as  illus- 
trated above  in  boys  aged  11,  is  due  to  the  preponderance  in 
the  higher  grades  of  the  well  nourished  children  of  the  rich. 
This  may  be,  and  probably  is,  a  factor  in  the  phenomenon, 
but  is  surely  only  a  partial  influence. 

For  when  children  of  the  same  age  and  as  nearly  as  possible 
of  the  same  social  class  are  weighed  and  the  weights  dis- 
tributed by  school  grade,  it  is  found  that  they  follow  the  law 
established  for  the  whole  material  irrespective  of  social  condi- 
tion. A  glance  at  Plate  XLVI,  derived  from  Table  No.  36, 
will    convince    the    reader    of   the   truth    of    this    statement. 


Porter  —  The  Growth  of  St.  Louis  Children. 


337 


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Trans.  Acad.  Sci.  of  St.  Louis. 


Further  evidence  is  afforded  by  Table  No.  37,  in  which  the 
daughters  of  professional  men  are  divided  into  two  equal 
groups,  in  the  manner  explained  on  page  177  of  The  Physical 
Basis  of  Precocity  and  Dullness,  one  group  containing  the 
fifty  per  cent  who  are  found  in  the  upper  grades,  the  other 
the  fifty  per  cent  found  in  the  lower  grades.     It  should  be 

TABLE   No.   37. 

Median  Weight   of  the   Daughters   of   Professional  Men  Distrib- 
uted BY  School  Grade. 


■*H 

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7 

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8 

52.5 

9 

53.5 

10 

57.5 

11 

58.0 

12 

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School  Grades. 


Kg.,  10  I. 

Kg.,  97  I. 

I,  69  II. 

I,  II,  48  III. 

I,  II,  III,  28  IV. 

I,  II,  III,  81  IV. 

II,  III,  IV,  78  V, 


Median 

Weight. 

(Kilogram's) 

Median 

Weight. 

(Kilogram's) 

20.29 

20.81 

22.13 

23.75 

24.52 

25.07 

27.19 

27.64 

28.76 

31.27 

33.65 

34.05 

38.46 

39.55 

School  Grades. 


90  I,  II. 

3  I,  II,  III. 

31  II,  III,  IV,  V. 

52  III,  IV,  V,  VI. 

72  IV,  V,  VI,  VII. 

19  IV,  V,  VI,  VII. 

22  V,VI,VII,VIII. 


Number  of 
Observa- 
tions. 

50 
52.5 
53.5 
57.5 

58.0 

50 

55.5 

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9 
10 
11 
12 
13 


remarked  that  this  method  of  division  diminishes  the  cou- 
spicuousness  of  the  difi'erence  between  lower  and  higher 
grades  by  not  presenting  the  weights  for  outlying  grades,  but 
for  a  small  number  of  observations  it  is  much  more  reliable 
than  the  method  of  which  Table  No.  36  is  an  illustration. 

The  results  of  this  study  of  the  weights  of  girls  from 
the  same  social  class  distributed  by  school  grade  confirm  the 
conclusion  reached  in  the  publications  cited  above,  namely 
that  successful  pupils  are  larger  than   the  unsuccessful. 


CHAPTER    IX. 

THE  APPLICATION  TO  INDIVIDUAL  SCHOOL  CHILDREN  OF  THE  MEAN  VALUES 
DERIVED  FROM  ANTHROPOLOGICAL  MEASUREMENTS  BY  THE  GENERALIZING 
METHOD. 

The  data  for  the  studies  described  in  this  work  can  be  col- 
lected either  bv  the  "  generalizing  "  or  by  the  "  individualiz- 
ing "  plan.  In  the  former,  a  great  number  of  measurements 
is  made  but  once  on  individuals  of  different  ages,  and  the 
measurements  classified  according  to  age.  In  the  lattei;,  the 
same  individuals  are  measured  yearly  or  oftener  during  their 
period  of  growth,  and  the  measurements  classified  also  by 
age.  The  generalizing  method,  the  one  pursued  in  the  present 
investigation,  is  rapidly  and  easily  carried  out,  whereas  the 
individualizing  method  demands  for  its  execution  exceptional 
opportunities  and  exceptional  patience,  requiring  not  only 
that  the  measurements  be  made  and  the  records  kept  through 
two  decades,  but  that  the  number  of  children  measured  in  the 
early  years  of  this  long  period  be  very  great,  lest  death  and 
desertion  so  thin  the  ranks  that  those  remaining  to  the  end 
shall  be  too  few  to  yield  trustworthy  conclusions.  Both 
methods,  when  applied  to  the  same  material,  give  identical 
results  with  regard  to  means,  including  those  of  subdivisions 
as  well  as  those  of  the  whole  number  of  observations.  The 
individualizing  method  does  more. 

The  importance  of  the  individualizing  method  has  been  much 
emphasized,  for  the  reason  that  it  can  give  information  without 
which  the  laws  derived  from  means  cannot,  in  the  present  state 
of  knowledge,  be  applied  to  individuals.  Before  this  appli- 
cation can  be  made,  it  is  necessary  to  know  the  degree  of  prob- 
ability that  an  individual,  who  at  a  given  age  stands  at  a  certain 
deviation  from  the  mean  of  any  dimension  will  show  the  same 
deviation  at  other  ages;  for  example,  the  degree  of  probability 
that  a  girl  whose  height  at  age  8  is  122.06  cm.,  and  who 
therefore  deviates  3.7  cm.,  or  +lcZ  from  the  mean  of  her  age 
(118.36  cm.),  will  deviate  to  the  same  degree  (-{-Id)  from 

(339) 


340  Trans.  Acad.  Sci.  of  St.  Louis. 

the  mean  height  throughout  her  growth.  In  that  case,  the 
law  of  growth  for  the  type  at  a  deviation  of  -\-ld  from  the 
mean  is  her  law  of  growth.  Otherwise,  she  is  an  exception 
and  practical  regulations  deduced  from  the  law  for  the  type 
cannot  be  safely  made  binding  on  her.  This  knowledge,  as 
has  just  been  said,  is  furnished  by  the  individualizing  method, 
while  the  generalizing  method  is  of  no  assistance  in  this  matter. 

The  application  to  individuals  of  the  law  of  growth  of  the 
mean  is  a  subject  of  immediate  practical  interest.  The  con- 
nection between  theory  and  practical  affairs  is  here  unusually 
short  and  clear.  Were  this  application  possible,  the  devia- 
tions of  children  from  the  laws  of  normal  growth  could  be 
quickly  recognized  and  largely  overcome,  the  evil  effect  of 
over  study  could  be  watched  and  intelligently  combated,  and 
systems  of  education,  no  longer  exacting  of  all  that  which 
should  be  exacted  only  from  the  mean,  could  be  rationally 
adapted  to  the  special  needs  of  the  exceptionally  weak  and 
the  exceptionally  strong. 

These  beneficent  reforms,  it  is  at  present  believed,  must 
await  the  slow  collection  of  data  by  the  individualizing 
method.  If  it  is  indeed  true  that  the  laws  of  growth  deter- 
mined for  the  mean  cannot  be  used  for  the  individual  until 
the  individualizing  method  has  established  the  probability 
of  each  individual  deviation  remaining  constant  throughout 
the  period  of  growth,  then  a  generation  must  elapse  —  so 
slow  is  the  gathering  of  data  by  this  method  —  before  the 
necessary  knowledge  is  in  our  hands.  I  hope  to  show  that 
this  long  waiting  is  unnecessary,  and  that  the  data  collected 
by  the  generalizing  method  may  be  used,  in  a  way  hitherto 
unrecognized,  for  the  making  of  standards  by  which  the 
deviation  of  an  individual  from  the  mean  of  his  age  may  be 
seen  to  be  normal  or  abnormal. 

Let  the  problem  be  clearly  understood.  The  question  is : 
this  boy  or  girl  is  above  or  below  the  mean  height,  or  weight, 
etc.,  of  his  or  her  age.  How  shall  it  be  known  that  this 
deviation  is  normal  or  abnormal?  There  has  been  hitherto 
no  satisfactory  reply  to  this  question.  A  vague  and  partial 
answer  is  possible  after  two  measurements  separated  by  at 
least  a  year's  interval.     If  the  deviation  is  the  same,  or  very 


Porter  —  The  Growth  of  St.  Louis  Children. 


341 


nearly  the  same,  at  both  measurements,  the  probability  is  that 
the  child  is  growing  normally.  This  probability  is  greater 
than  the  general  probability  that  a  normal  deviation  is  more 
likely  to  occur  than  an  abnormal  one,  but  its  numerical  value 
is  wholly  unknown.  If,  on  the  other,hand,  the  two  deviations 
are  unequal,  the  probability  is  that  the  greater  of  them  is 
abnormal,  but  the  numerical  value  is  here  also  unknown. 
How  definitely  the  individualizing  method  could  answer  this 
question  is  difficult  of  conjecture,  in  the  present  lack  of  data, 
but  certainly  no  answer  whatever  could  be  expected  except 
after  two  measurements  separated  by  a  year's  interval,  a  year 
in  which  the  unchecked  cause  of  an  abnormal  deviation  might 
inflict  an  irreparable  damage  on  the  organism.  Such  indefi- 
nite and  fragmentary  knowledge  can  never  be  the  basis  of  a 
practical  reform.  Any  solution  of  this  problem  which  shall 
gain  general  acceptance  must  be  easy  to  understand  and  easy 
to  apply,  and  must  give  the  probable  degree  of  abnormality^ 
of  any  observed  deviation.  These  conditions  are,  I  believes, 
fulfilled  b}'  the  following  method. 

According  to  the  theory  of  probabilities,  the  heights  of  a 
thousand  individuals  of  the  same  class  will  arrange  themselves 
as  follows:  — 


tween 

M+4(?        and        U+nd 

M+3d 

«          M-f4d 

M+2d           ' 

'          M+3cZ 

M+  d 

'          M+2d 

M 

'          M+  d 

M 

'          M—  d 

M—  d          ' 

M— 2d 

M-2d 

«          M—Sd 

M—3d 

'         M—id 

M—id          ' 

'          M — nd 

3 

individuals 

18 

67 

162 

250 

250 

162 

67 

18 

3 

where  M  =  the  mean  and  c?=the  probable  deviation. 
Let  these  be  divided  into  seven  groups:  — 


I. 

II. 

III. 

VI. 

V. 

IV. 

VII. 


All  individuals  betv^een 


M-}-nd      and 

M+3d 

21 

M+3d        " 

M+2d 

67 

M+2d        " 

M+  d 

162 

M 

Md=  d 

500 

M—  d 

M— 2d 

162 

M—2d       «' 

M-3d 

67 

M—Sd        " 

M—nd 

21 

342  Trans.  Acad.  Sci.  of  St.  Louis. 

The  mean  height,  weight,  girth  of  chest,  etc.,  of  each 
of  these  groups  at  any  age  will  be  the  type  of  a  certain 
deorree  of  deviation  from  the  mean  of  the  age.  That  is  to 
say,  the  weights,  etc.,  of  each  group  will  be  symmetrically 
distributed  above  and  below  the  mean  weight,  etc.,  of  the 
group  in  the  manner  already  illustrated  for  the  entire  undivided 
number  of  observations,  i.  e.,  the  entire  thousand.  Each 
group,  therefore,  will  be  characterized  by  a  physical  develop- 
ment definitely  determined  by  the  means  of  height,  weight 
and  other  physical  dimensions.  These  means,  taken  together 
form  the  type  or  norm  of  the  group.  The  individual  devia- 
tions from  this  norm  follow  the  theory  of  probability,  and 
the  degree  of  abnormality  presented  by  any  individual  devia- 
tion can  be  expressed  in  the  terms  of  this  theory.  An  exam- 
ple will  illustrate  this.  A  boy  X  shows  a  deviation  in  height 
of  -\-1.5d  from  the  mean  height  of  his  age.  He  falls  therefore 
in  Group  III.  The  boys  in  this  group  possess  a  mean  weight 
of  M  kilogrammes,  with  a  probable  deviation  of  zLd ;  that 
is,  boys  between  d  and  2d  taller  than  the  norm  of  their  age 
should  weigh  M±f^  kilogrammes.  In  like  manner,  they 
should  have  a  girth  of  chest  of  M:hd  centimetres,  and  a 
span  of  arms  of  M±tZ  centimetres,  and  so  on.  If  the 
weight,  etc.,  of  the  boy  X  coincide  with  the  means  of  his 
group  (Group  III)  his  physique  is  normal,  the  accuracy  of 
this  conclusion  being  proportionate  to  the  number  of  different 
dimensions  on  which  it  is  based.  If  the  boy  X  deviate  more 
than  zLld  from  the  mean  in  one  or  more  dimensions,  his 
development  is  abnormal,  and  the  degree  of  abnormality  is 
measured  by  the  amount  of  his  deviation. 

The  necessity  of  choosing  some  one  dimension  as  the  basis 
of  such  a  system  is  self-evident.  There  are  good  reasons, 
partly  theoretical  and  partly  practical,  why  height  rather  than 
weight  should  be  taken  as  a  basis.  Height  is  more  stable, 
less  liable  to  irrelevant  fluctuations,  than  weight.  An  excess 
in  weight  can  be  reduced ;  a  child  whose  weight  is  out  of  pro- 
portion to  its  height  may  be  brought  into  proportion  by  suitable 
diet  and  exercise ;  but  height,  once  attained,  cannot  be  reduced, 
nor  can  the  growth  in  height  be  easily  influenced.  Practically, 
therefore,  the  physical  trainer  must  be  content  to  bring  the 


Porter  —  The  Growth  of  St.  Louis  Children.  343 

weight,  girth  of  chest,  strength  of  squeeze  and  other  physical 
dimensions  up  to  the  mean  development  which  corresponds  to 
the  height  of  the  child.  Experience  has  abundantly  shown 
that  the  relation  of  weight  to  height  is  of  great  importance  to 
health,  life  insurance  companies  declining  to  receive  applicants 
whose  weight  falls  much  below  the  standard  weight  of  their 
height.  For  these  reasons,  height  should  be  preferred  as  the 
basis  of  the  system . 

The  question  whether  any  given  deviation  is  normal  or 
abnormal  is  answered  by  this  system  in  two  ways  :  in  respect 
of  height,  by  the  degree  of  deviation  from  the  mean  or  norm 
of  the  whole  number  of  observations  ;  in  respect  of  other 
dimensions,  by  the  degree  of  deviation  of  the  weight,  girth  of 
chest,  etc.,  from  the  mean  weight  or  girth  of  chest  corre- 
sponding to  the  height  of  the  individual  under  examination, 
this  normal  weight,  etc.,  being  determined  with  sufficient 
exactness  by  taking  the  means  and  probable  deviations  of  the 
group  in  which  the  height  falls.  It  is  evident  that  all  cases 
included  within  M±c^  must  be  termed  normal,  for  the  chances 
are  even  that  any  individual  measurement  in  a  series  will  fall 
within  M±tZ  and  are  against  its  exceeding  these  limits,  being 
4.64  against  1  that  it  will  fall  at  M±2d. 

Strictly  speaking,  all  abnormal  deviations  in  any  dimension 
are  probably  unhealthful,  yet  an  important  difference  exists 
in  this  respect  between  abnormal  deviations  in  height  and 
abnormal  deviations  in  weight,  girth  of  chest,  etc.,  as  related 
to  height.  It  cannot  be  doubted  that  abnormal  height  is 
probably  (using  the  word  in  its  technical  sense)  a  disadvan- 
tage. The  potential  energy  of  the  body  is  converted  into 
mechanical  labor  and  heat,  by  far  the  greater  expenditure 
taking  the  latter  form.  In  the  adult,  the  total  expenditure 
in  the  form  of  heat  is  about  2,700  calories  in  24  hours 
(Helmholtz),  of  which  80.1  per  cent  escape  in  radiation,  con- 
duction and  evaporation  from  the  skin.  Thus  the  superficies 
of  the  body  plays  a  great  part  in  the  dissipation  of  energy. 
The  superficies  is  greater,  usually,  in  tall  children  than  in 
short,  a  difference  of  special  importance  in  the  young,  in 
whom  metabolism  is  much  more  active  than  in  the  adult. 
More  heat  is  therefore  lost  by  the  abnormally  tall  than   by 


344  Trans.  Acad.  Sci.  of  St.  Louis. 

those  of  normal  height.  There  is  a  disadvantage  also  in  the 
loss  by  mechanical  labor.  Greater  height  entails  increased 
work  on  the  heart  and  on  the  skeletal  muscles.  In  short, 
increased  loss  of  energy  goes  hand  in  hand  with  increase  in 
height.  Hence  in  the  tall  the  necessity  for  a  physical 
development  which  shall  be  so  much  above  the  mean  as  to 
compensate  their  greater  loss  of  energy.  In  growing  children 
not  only  must  there  be  compensation  for  the  expenditure  of 
energy,  but  there  must  be  also  energy  stored  in  the  increase 
of  tissue  which  constitutes  growth. 

If  the  greater  demands  of  tall  children  are  balanced  by  a 
correspondingly  greater  income  of  energy,  a  normal  equilib- 
rium or  "  health  "  is  preserved.  It  should  be  clearly  recog- 
nized that  this  equilibrium  is  unaffected  by  the  absolute 
height  and  is  dependent  only  on  the  relation  between  height 
and  the  other  physical  dimensions.  Consequently  health  is 
as  possible  in  tall  children  as  in  those  of  normal  height, 
although  less  probable,  for  the  chances  against  a  compensatory 
development  of  weight  and  other  dimensions  increase  very 
rapidly  with  the  deviation  of  the  height  from  the  norm. 
The  absolute  height  of  an  individual  is  of  very  secondary 
interest  from  a  practical  point  of  view,  because  it  is  not  nec- 
essarily a  state  of  ill  health,  whereas  the  development  of 
weight,  girth  of  chest,  etc.,  in  proportion  to  height  is  of 
supreme  interest.  A  lack  of  proportion  between  height 
and  other  physical  dimensions  is  itself  ill  health.  The  ten- 
dency of  organisms  to  adopt  ends  to  means  is  strong,  and  an 
imperfect  compensation  may  suffice  for  most  demands.  A 
heart  in  which  an  hypertrophy  of  the  left  ventricle  has  par- 
tially compensated  an  insufficiency  of  the  mitral  valve  may 
beat  regularly  enough  for  ordinary  exertions,  and  yet  fail 
utterly  when  its  possessor  is  forced  suddenly  to  ascend  a 
height  or  to  make  any  other  unusual  exertion.  So  a  tall  child 
may  have  a  sufficient  income  of  energy  to  meet  the  demands 
of  a  wisely  regulated  life,  and  sink  under  the  burden  of 
unusual  tasks. 

It  has  been  shown  in  the  foregoing  pages  that  the  means 
derived  from  anthropometrical  metrical  measurements  by  the 
generalizing   method  can  be  used  to   determine  whether  the 


Porter  —  The  Groiolh  of  St.  Louis  Children.  345 

weight  and  other  physical  dimensions  of  an  individual  are 
normal  in  relation  to  height,  and  it  has  been  pointed  out  that 
this  normal  relation  constitutes  health.  It  follows  that  the 
normal  amount  of  labor  cannot  be  exacted  without  injury 
from  those  in  whom  this  equilibrium  is  wanting.  These 
facts  must  therefore  be  taken  into  account  in  a  rational 
school  system,  and  it  should  now  be  made  plain  how  this  is  to 
be  done. 

All  systems  of  education  have  for  their  object  the  largest 
possible  development  of  individual  minds.  In  large  schools 
the  tasks  by  which  this  development  is  promoted  are  those 
which  secure  from  the  child  of  mean  ability  its  maximum 
mental  output.  In  practice  they  are  determined  by  examina- 
tions. Hence  the  existence  in  every  educational  institution 
of  classes  based  on  the  mental  output  of  the  mean  pupil,  and 
related  to  age  only  in  that  the  output  fixed  as  the  standard  of 
any  class  is  necessarily  found  more  often  at  a  certain  age  than 
at  other  ages.  Thus  there  exists  a  mean  age  for  each  class; 
the  greater  number  of  pupils  at  any  age  is  found  in  the  same 
class,  while  some  have  advanced  beyond,  and  others,  equally 
old,  have  not  yet  come  so  far  as  this  class.  On  an  average, 
those  who  have  advanced  beyond  the  greater  number  of  their 
age  are  precocious,  that  is,  possess  more  than  the  mean  capac- 
ity for  mental  labor,  while  those  who  are  less  advanced  are 
dull,  possessing  less  than  the  mean  capacity.  It  has  been 
demonstrated  that  there  is  a  physical  basis  for  precocity  and 
dullness :  ^  when  numbers  sufficiently  large  for  statistical 
purposes  are  employed,  it  is  seen  that  precocious  pupils  are 
of  greater  mean  weight,  height,  etc.,  than  the  mean  pupils 
and  that  the  latter  are  heavier  and  taller  that  the  dull.  The 
mental  output  is  therefore  directly  related  to  the  physical 
condition  of  the  pupils.  The  mean  height,  weight,  girth  of 
chest,  etc.,  in  any  grade  is  the  mean  physical  development 
corresponding  to  the  mental  output  of  the  grade.  It  follows 
that  those  who  do  not  possess  this  development  cannot  with- 
out abnormal  strain  do  the  work  exacted  in  this  grade.  On 
the    other   hand,  pupils  who    possess    more    than    the  mean 


1  See  Chapter  VIII,  page  335  et  seq. 


346  Trans.  Acad.  Sci.  of  St.  Louis. 

physical  development  of  their  age  should  be  capable  of  more 
than  the  mean  labor.  Yet  the  management  of  this  latter 
class  presents  but  few  difficulties,  whereas  the  former  class 
cannot  be  too  carefully  protected. 

The  consequences  of  continued  overstrain  in  a  growing  boy 
or  girl  are  most  unhappy.  The  curves  of  growth  in  height 
and  weight  of  the  mean  child  are  characteristic.  The  quick 
rise  to  age  7  or  8,  the  slower  ascent  to  age  11  in  girls  and  13 
in  boys,  the  remarkable  three  years  of  accelerated  develop- 
ment preceding  puberty,  and,  finally,  the  rapid  decrease  in 
the  rate  of  growth  as  full  development  approaches  express 
the  normal  development  of  the  type  and,  presumably,  the 
normal  development  of  the  individual.  Overwork  may  cause 
a  temporary  or  a  permanent  deviation  in  these  curves.  It  is 
probable,  though  not  certain,  that  a  temporary  loss  consequent 
on  a  slight  overstrain  may  not  lower  the  final  outcome  of  the 
development,  but  there  can  be  no  doubt  as  to  the  result  of  a 
prolonged  strain.  In  such  a  case,  the  probability  is  strong 
that  the  whole  subsequent  curve  will  be  turned  out  of  its 
course.  A  prolonged  strain  in  a  growing  child  harms  for 
life  and  leaves  a  mark  which  can  never  be  effaced.  The 
danger  is  greatest  in  the  periods  of  quickest  development, 
particularly  great  in  the  prepubertal  period.  It  is  a  sufficient 
commentary  on  the  evils  of  the  present  educational  methods 
that  during  these  very  years  the  undiscriminating  routine  of  a 
system  devised  for  the  average  pupil  is  most  inflexibly  applied 
to  weak  and  strong  alike. 

Overstrain  can  often  be  recognized  both  by  subjective  and 
objective  symptoms.  Subjective  symptoms,  however,  are 
frequently  obtained  with  difficulty,  especially  in  pupils  who 
are  unusually  ambitious  and  who  overstudy  from  choice.  An 
objective  symptom  must  therefore  be  found — a  symptom 
easily  demonstrated  and  almost  never  wanting.  Such  a 
symptom  is  the  failure  to  gain  weight  at  the  normal  rate.  A 
persistent  loss  of  weight  in  an  adult  is  regarded  as  a  matter 
of  grave  concern;  the  persistent  failure  of  a  child  to  make 
the  normal  gain  in  weight  is  no  less  grave.  It  is  not  pretended 
that  the  failure  to  gain  weight  always  accompanies  overstrain, 
but   it  is  claimed  that  the  number  of  exceptions  is  small  and 


Porter  —  The  Growth  of  St.  Louis  Children.  347 

that  frequent  weighing  is  the  most  practical  and  on  the  whole 
the  most  certain  method  of  detecting  the  presence  of  influences 
that  are  working  injury  to  the  development  of  the  child. 
The  skillful  breeder  of  cattle  depends  on  systematic  weighing 
to  inform  him  if  his  efibrts  are  meeting  with  success,  but 
children  are  left  to  grow  at  haphazard. 

It  is  not  enough  that  overstrain  should  be  recognized  by  the 
harm  it  has  done.  The  child  should  be  guarded  aorainst  the 
possibility  of  harm.  The  anthropometrical  system  proposed 
ofi'ers  a  means  of  doing  this.  It  infallibly  discovers 
the  children  whose  physical  development  is  below  the 
standard  of  their  age.  It  no  less  certainly  indicates  the 
physical  development  which  most  often  accompanies  the 
power  to  do  the  mental  work  of  any  grade.  It  therefore 
divides  the  pupils  into  two  bodies;  those  physically  compe- 
tent and  those  physically  incompetent  for  a  clearly  defined 
degree  of  mental  exertion.  When  working  with  great  num- 
bers, the  infallibility  of  this  system  is  practically  absolute  and 
theoretically  almost  absolute.  When  applied  to  individuals, 
errors  will  certainly  occur,  but  the  number  of  errors  will 
according  to  the  laws  of  probability  be  less  than  the  number 
of  correct  conclusions,  and  these  errors  cannot  influence  the 
great  fact  that  such  a  system  is  competent  to  call  attention  to 
the  children  who  will  probably  be  unable  to  do  the  normal 
work  of  their  age  without  injury.  Each  individual  case  must 
then  be  treated  on  its  own  merits. 

The  proposed  system  of  physical  examination  requires:  — 

I.  The  collection  of  sufficiently  extensive  data  by  the  gen- 
eralizing method. 

II.  The  determination  of  the  means  and  the  probable 
deviations  of  height,  weight,  girth  of  chest,  strength  of 
squeeze,  etc.,  for  each  age. 

III.  The  division  of  the  individuals  at  each  age  into  groups 
in  terms  of  the  probable  deviation  from  the  mean  height,  as 
illustrated  above,  and  the  calculation  of  the  mean  and  prob- 
able deviation  of  the  weight,  girth  of  chest,  etc.,  of  each 
group. 

IV.  The  determination  of  the  mean  physical  development 
of  the  pupils  in  each  class  or  grade  of  the  school  system. 


348  Trans.  Acad.  Sci.  of  St.  Louis. 

V.  The  physical  examination  of  each  applicant  for  entrance 
to  any  grade. 

These  data  permit  the  enforcement  of  the  following  regula- 
tion :  That  no  pupil  whose  physical  development  varies  more 
than  ±cZ  from  the  weight,  etc.,  of  the  mean  pupil  of  his 
height  in  a  class  which  his  mental  output  would  otherwise 
entitle  him  to  enter,  shall  be  admitted  to  that  class,  unless 
with  the  approval  of  a  medical  expert,  if  possible  a  regularly 
appointed  school  physician,  who  shall  testify  that  the  pupil's 
strength  will  be  equal  to  the  strain. 


TABLES  NO.  38  TO  51. 

The  tables  which  follow  this  page  repeat  some  of  the 
more  commonly  used  statistical  values  in  a  form  which  admits 
of  ready  reference  and  comparison.  Such  are  the  average, 
probable  error  of  the  average,  probable  deviation,  median  or 
50  percentile  grade  and  median  minus  average  values.  Yet 
these  tables  are  by  no  means  summaries  of  the  statistical  calcu- 
lations of  the  investigation,  since  they  omit  much  that  is  given 
in  the  foregoing  pages.  They  contain,  moreover,  not  a  little 
new  matter.  The  relation  of  probable  deviation  to  average, 
relation  of  average  to  height  standing,  relative  annual 
increase  of  average,  the  25  percentile  grade,  the  75  percentile 
grade,  the  cranial  indices  and  the  absolute  annual  increase  of 
average  of  strength  of  squeeze  and  of  measurements  of  the 
head  and  face  are  here  presented  for  the  first  time. 

Some  of  this  material  has  been  already  discussed  in  this 
paper.  Some  is  reserved  for  future  discussion.  One  series, 
the  relation  of  probable  deviation  to  average,  was  treated  at 
some  length  in  ray  paper  on  "  The  relation  between  the 
growth  of  children  and  their  deviation  from  the  physical  type 
of  their  sex  and  age,"  Transactions  of  the  Academy  of  Science 
of  St.  Louis,  Vol.  VI,  No.  10,  pp.  233-250,  November  14, 
1893,  to  which  the  reader  is  referred. 

Five  dynamometers  were  used  in  testing  the  strength  of 
squeeze ;  they  were  distinguished  by  the  first  five  letters  of 
the  alphabet ;  A  and  D  were  graduated  alike  ;  C  and  E  were 
also  alike  but  differed  from  A  and  D,  and  B  differed  from  all 
the  others.  The  original  values  obtained  with  these  various 
instruments  are  set  down  in  Tables  No.  45  and  46  ;  from  them 
were  made  Tables  No.  43  and  44,  by  reducing  the  arbitrary 
graduation  of  all  dynamometers  to  a  uniform  scale  in  kilo- 
grammes. 

(349) 


350 


Trans.  Acad.  Sci.  of  St.  Louis. 


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CORRIGENDA. 

Page  263.  Author's  name  omitted :  W.  To wnsend  Porter. 

288.  Boys,  aged  16,  hair-line  to  point  of  chin  should  read  0.425  mm. 

297.  Boys,  aged  10,  median  minus  average  should  read  —  0.07  cm. 

313.  Boys,  aged  8,  50  percentile  grade  should  read  119.77  cm. 

313.  Girls,  aged  8,  50  percentile  grade  should  read  118.74  cm. 

315.  Girls,  aged  6,  50  percentile  grade  should  read  107.29  cm. 

315.  Girls,  aged  8,  50  percentile  grade  should  read  118.33  cm. 

321.  Girls,  aged  14,  number  of  observations  should  read  997. 


(370) 


LIST   OB^   PLATES. 

Plate  I.  The  calculated  and  the  observed  distribution  of  the  height 
standing  of  2192  St.  Louis  school  girls,  aged  8. 
II.  Median  minus  average  values   (weight,   height,  height 
sitting,  span  of  arms) . 

III.  Median  minus  average  values  (chest-girth  and  strength 

of  squeeze). 

IV.  Median  minus  average  values  (head  and  face  measure- 

ments) . 
V.  Boys'  weight  (percentile  grades) . 
VI.  Girls'  weight  (percentile  grades) . 
VII.  Boys'  height  standing  (percentile  grades). 
VIII.  Girls'  height  standing  (percentile  grades) . 
IX.  Boys' height  sitting  (percentile  grades). 
X.  Girls' height  sitting  (percentile  grades). 
XL  Boys'  span  of  arms  (percentile  grades) . 
XII.  Girls'  span  of  arms  (percentile  grades). 

XIII.  Boys'  girth  of  chest  (percentile  grades) . 

XIV.  Girls'  girth  of  chest  (percentile  grades) . 
XV.  Boys'  length  of  head  (percentile  grades). 

XVI.  Girls'  length  of  head  (percentile  grades). 
XVII.  Boys'  width  of  head  (percentile  grades). 
XVIII.  Girls'  width  of  head  (percentile  grades). 
XIX.  Boys'  height  of  face  from  root  of  nose  to  point  of  chin 
(percentile  grades) . 
XX.  Girls'  height  of  face  from  root  of  nose  to  point  of  chin 
(percentile  grades) . 

XXI.  Boys'  width  of  face  (percentile  grades) . 

XXII.  Girls'  width  of  face  (percentile  grades). 

XXIII.  Boys'  height  of  face  from  hair-line  to  point  of  chin  (per- 

centile grades). 

XXIV.  Girls'  height  of  face  from  hair-line  to  point  of  chin  (per- 

centile grades). 
XXV.  Weight,  75,  50  and  25  percentile  grades. 
XXVI.  Height  standing,  75,  50  and  25  percentile  grades. 
XXVII.  Height  sitting,  75,  50  and  25  percentile  grades. 
XXVIII.  Span  of  arms,  75,  50  and  25  percentile  grades. 
XXIX.  Girth  of  chest,  75,  50  and  25  percentile  grades. 
XXX.  Mean  expansion  of  chest. 
XXXI.  Mean  strength  of  squeeze. 
XXXII.  Length  of  head,  75,  50  and  25  percentile  grades. 

XXXIII.  Width  of  head,  75,  50  and  25  percentile  grades. 

XXXIV.  Height  of  face  from  root  of  nose  to  point  of  chin,  75,  50 

and  25  percentile  grades. 

(371) 


372 


List  of  Plates. 


Plate  XXXV. 
XXXVI, 

xxxvir. 

XXXVIII. 

XXXIX. 

XL. 

XLI. 

XLII. 

XLIII. 

XLIV. 

XLV. 
XLVI 


Width  ol  face,  75,  50  and  25  percentile  grades. 

Heiglit  of  face  from  hair-line  to  point  of  chin,  75,  50  and 
25  percentile  grades. 

Percentile  grades,  weight. 

Percentile  grades,  height  standing. 

Percentile  grades,  height  sitting. 

Percentile  grades,  span  of  arms. 

Percentile  grades,  girth  of  chest. 

Absolute  annual  increase  (height  standing,  weight,  span 
of  arms). 

Absolute  annual  increase  (height  sitting,  girth  of  chest, 
strength  of  squeeze). 

Relative  annual  increase  (strength  of  squeeze,  weight, 
height  standing,  height  sitting,  span  of  arms,  chest- 
girth). 

Relation  of  average  weight,  span  of  arms,  girth  of  chest, 
etc.,  to  average  height. 

The  weights  of  daughters  of  manual  tradesmen  distrib- 
uted by  school  grade. 


INDEX  OF  TABLES. 

PAGE. 

No.  1.  The  distribution  of  2000  measurements  of  the  same  quantity 
when  the  deviation  of  the  individual  observations  from  the 
trne  value  of  the  measured  quantity  is  due  to  purely  accidental 
causes 277 

2.  Heights  of  United  States  recruits 278 

3.  Observed  distribution  of  the  heights  of  2192  St.  Louis  school 

girls,  aged  8 279 

The  calculation  of  the  average  height  of  St.  Louis  school  girls, 
aged  9 280 

5.  The  calculation  of  the  probable  deviation  (d)  from  the  average 

height  (118.36  cm.)  of  2193  girls,  aged  8 283 

6.  Stieda's  table  for  calculating  the  number  of  observations  at  any 

distance  from  the  mean  or  average  within  the  limits :  M  -\-  5d 
and  M  —  5d 284 

7.  The  theoretical  and  the  observed  distribution  of  the  heights  of 

2192  girls,  aged  8 286 

8.  The  percentile  distribution  of  the  heights  of  girls,  aged  9 287 

9.  The  probable  error  of  the  average 288 

10,  The  probable  deviation  (d)  from  the  average 291 

11.  Median  minus  average  values 296,  297 

12,  Sums  of  median  minus  average  values 300 

13.  A  comparison  of  weights  of  the  daughters  of  manual  tradesmen 

with  the  weights  of  the  daughters  of  professional  men  and 

merchants 305 

14.  The  percentile  distribution  by  school  grade  of  the  daughters  of 
merchants  and  professional  men  (i.  e.  favored  classes)  com- 
pared with  that  of  the  daughters  of  manual  tradesmen  (hand- 
workers)     307 

15.  The  weights  of  girls  whose  parents  were  born  in  Germany  com- 

pared with  the  weights  of  girls  whose  parents  were  born  in 
the  United  States 309 

16.  The  weights  of  boys  whose  parents  were  born  in  Germany  com- 

pared with  the  weights  of  boys  whose  parents  were  born  in 
the  United  States 310 

17.  The  weight  (percentile  grades) 312 

18.  The  height  standing  (percentile  grades) 313 

19.  The  height  sitting  (percentile  grades) 314 

20.  The  span  of  arms  (percentile  grades) 315 

21.  The  girth  of  chest  at  full  inspiration  (percentile  grades) 316 

22.  The  girth  of  chest  at  full  expiration  (percentile  grades) 317 

23.  The  girth  of  chest  midway  between  full  inspiration  and  full  ex- 

piration (percentile  grades) 318 

24.  The  length  of  head  (percentile  grades) 319 

(373) 


374  Index  of  Tables. 

PAGE. 

No.  25.  The  width  of  head  (percentile  grades) 320 

26.  The  height  of  face  from  root  of  nose  to  point  of  chin  (percentile 

grades) 321 

27.  The  width  of  face  (percentile  grades) 322 

28.  The  height  of  face  from  hair-line  to  point  of  chin  (percentile 

grades 323 

29.  Ages  at  which  girls  begin  and  cease  to  be  larger  than  boys 324 

30.  The  absolute  annual  increase  in  height  standing 328 

31.  The  absolute  annual  increase  in  weight 329 

32.  The  absolute  annual  increase  in  span  of  arms 330 

33.  The  absolute  annual  increase  in  height  sitting 331 

34.  The  absolute  annual  increase  in  girth  of  chest 332 

35.  Median  weight  of  boys  aged  11  distributed  by  school  grade 335 

36.  Median  weight  of  the  daughters  of  manual  tradesmen  distrib- 

uted by  school  grade 337 

37.  Median  weight  of  the  daughters  of  professional  men  distributed 

by  school  grade 338 

38.  The  height  standing 350 

39.  The  weight 351 

40.  The  height  sitting 352 

41.  The  span  of  arms 353 

42.  The  girth  of  chest  midway  between  inspiration  and  expiration . .  354 

43.  The  strength  of  squeeze,  right  hand 355 

44.  The  strength  of  squeeze,  left  hand 356 

45.  The  strength  of  squeeze,  right  hand 357 

46.  The  strength  of  squeeze,  left  hand • 358 

47.  The  length  of  head 359 

48.  The  width  of  head 360 

49.  The  height  of  face  from  root  of  nose  to  point  of  chin 361 

50.  The  width  of  face 362 

51 .  The  height  of  face  from  hair-line  to  point  of  chin 363 


GENERAL    INDEX. 

PAGE . 

Accidental  influences 275 

Acuteness  of  vision* 271 

American  girls'  weights 309 

American  boys'  weights 310 

Annual  increase — 

Absolute 327,  328  to  332,  Plates  XLII,  XLIII 

Kelative 327,  333,  Plate  XLIV 

Anthropometrical  series 277 

Anthropometrical  system  in  schools 341,  347 

Apparatus 269 

Assistants — 

Names 264 

Duties 268,  269 

Authorization  by  School  Board 263 

Average — 

Calculation 280 

Definition 280 

Deviation  from 291 

Error  of 287,  288 

Of  different  series 281 

Relation  to  mean 294 

Bibliography 364 

Birth-place  of  pupils 309 

Bowditch  on  median  and  average 294 

Chart  of  days 268 

Chest  expansion Piate  XXX 

Chest-girth  at  full  expiration — 

Median  minus  average 296,  300,  Plate  III 

Method  of  measuring 271,  274 

Percentile  grades 311,  317 

Chest-girth  at  full  inspiration  — 

Median  minus  average 296,  300,  Plate  III 

Method  of  measuring 271,  274 

Percentile  grades 31 1,  31S 


*  The  acuteness  of  vision  of  St.  Louis  school  children  will  be  discussed  in 
a  separate  paper. 

(375) 


376  General  Index. 

PAGE. 

Chest-girth  midway  between  full  inspiration  and  full  expiration  — 

Absolute  annual  increase 332,  Plate  XLIII 

Median  minus  average 296,  354r 

Percentile  grades 311,  318,  354,  Plates  XIII,  XIV,  XXIX,  XLI 

Probable  deviation 291,  354 

Probable  error 288,  354 

Relation  to  height  standing 334,  354,  Plate  XLV 

Relation  of  probable  deviation  to  average 354 

Relative  annual  increase 327,  333,  354,  Plate  XLIV 

Collection  of  data = 26» 

Constant  causes > 275 

Curves  all  printed 264 

Deafness  unsuspected 273 

Difference  of  individual  from  type 292 

Distribution  of  observations  — 

About  middle  value ■ 277 

According  to  Thoma 277 

Girls'  heights 279 

Of  1000  individuals 341 

Theoretical  and  observed 283,  286,  Plate  I 

Duration  of  investigation 26* 

Errors  — 

Constant 275,  292 

Of  observation 292 

Physiological 292 

Variable 275,  292 

Face  (see  Height  of  face  and  Width  of  face) . 

Gallon's  percentile  grades 286,  287 

Generalizing  method 263,  294,  33» 

German  parentage  and  vreight 309,  310 

Girls  larger  than  boys  of  same  age 324,  32i 

Head  (see  Length  of  head  and  "Width  of  head). 

Head  measurers  269 

Hearing  tests 272 

Hearing  tests  impracticable 273 

Height  — 

Abnormal  height  a  disadvantage 333,  343 

Basis  of  a  system  of  standards 342 

Of  United  States  recruits 278 

Height  of  face  from  hair-line  to  point  of  chin  — 

Absolute  annual  increase 363 

Median  minus  average 296,  Plate  IV 

Method  of  measuring 273 

Percentile  grades 311,  323,  363,  Plates  XXIII,  XXIV,  XXXVI 


General  Index.  377 

PAGE. 

Height  of  face  from  hair-line  to  point  of  chin  —  Continued. 

Probable  deviation 291,  363 

Probable  error 288,  363 

Relation  of  probable  deviation  to  average 363 

Relation  to  height  standing 334,  363,  Plate  XLV 

Relative  annual  increase 363 

Height  of  face  from  root  of  nose  to  point  of  chin  — 

Absolute  annual  increase 361 

Median  minus  average 296,  Plate  IV 

Method   of  measuring 273 

Percentile  grades 311,  321,  361,  Plates  XIX,  XX,  XXXIV 

Probable  deviation 291,  361 

Probable  error 288,  361 

Relation  to  probable  deviation  to  average 361 

Relation  to  height  standing 334,361,  Plate  XLV 

Relative  annual  increase 361 

Height  sitting  — 

Absolute  annual  increase 327,  331,  Plate  XLIII 

Median  minus  average 296,  352,  Plate  II 

Method  of  measuring 270 

Percentile  grades 311,  314,  352,  Plates  IX,  X,  XXVII,  XXXIX 

Probable  deviation 291,  352 

Probable  error 288,  352 

Relation  of  probable  deviation  to  average 352 

Relation  to  height  standing , 334,  352,  Plate  XLV 

Relative  annual  increase  327,  333,  352,  Plate  XLI V 

Height  standing  — 

Absolute  annual  increase 327,  328,  Plate  XLII 

Distribution  of,  in  girls  aged  8 286,  Plate  I 

Median  minus  average 296,  350,  Plate  II 

Method  of  measuring 270 

Percentile  grades 311,  313,  350,  Plates  VII,  VIII,  XXVI,  XXXVIII 

Probable   deviation 291,  350 

Probable   error 288,  350 

Ratio  to  other  physical  measurements 334,  Plate  XLV 

Relation  of  probable  deviation  to  average 350 

Relative  annual  increase 327,  333,  350,  Plate  XLIV 

Herschel  on  means o 294 

Indices  — 

Cranial 360 

Facial 362 

Individualizing  method 294,  339,  340 

Influences  affecting  measurements 275,  276 

Instructions  to  observers 269 

Length  of  head  — 

Absolute  annual  increase 359 

Median  minus  average 296,  Plate  IV 

Method  of  measuring 272 


378  General  Index. 

PAGE. 

Length  of  head  —  Continued. 

Percentile  grades 311,  319,  359,  Plates  XV,  XVI,  XXXII 

Probable  deviation 291,  359 

Probable  error 288,  359 

Eelation  of  probable  deviation  to  average 35^ 

Relation  to  height  standing 334,  359,  Plate  XLV 

Relative  annual  increase 359 

Loans  and  gifts 264 

Material  of  investigation  — 

Limitations 294 

Trustworthiness 290 

Manual  tradesmen 303 

Manual  tradesmen's  daughters  — 

Relative  number 307,  308 

Weights 305,  337 

Mean  (see  Median  value"). 

Median  value  — 

Advantage  over  average 294,  298 

Application  to  individuals 293,  294,  339,  340 

Calculation 281 

Definition 279,  281 

Minus  average 296>  298,  299,  300,  Plates  II,  III,  IV 

Uses  limited 294 

Mental  labor  and  physical  development 335 

Method  of  collecting  measurements 263 

Middle  value  — 

Definition 279 

Uses 293 

Nationality,  infiuence  on  weight 309 

Number  of  children  measured 268 

Occupation  of  parents 302 

Overstrain 346 

Percentile  grades — 

Calculation 286 

Plates V  to  XLI,  inclusive 

Tables 312  to  323  and  350  to  363,  inclusive 

Uses 311 

Plates,  List  of 371 

Printed  "forms  "  employed 265,  267,  269 

Probable  deviation — 

Calculation 282 

Definition    282 

From  average 291 

From  mean 284 

Table 291 

Probable  error  of  average- 
Calculation  287 

Table •- 288 


General  Index.  379 

PAGE. 

Professional  men  and  merchants 302 

Daughters'  weights 305,  306,  338 

Quetelet's  law 278 

Kate  of  growth 327 

Schools  measured 266 

Sexual  difEerences  in  growth 324 

Social  status  influences  weight 305,  310,  336,  338 

Span  of  arms  — 

Absolute  annual  increase 327,  330,  Plate  XLII 

Median  minus  average 296,  Plate  II 

Method  of  measuring 270 

Percentile  grades 311,  315,  353,  Plates  XI,  XII,  XXVIII,  XL 

Probable  deviation 291,  353 

Probable  error 288,  353 

Kelation  of  probable  deviation  to  average 353 

Eelation  to  height  standing 334,  353 

Eelative  annual  increase 327,  333,  353,  Plate  XLIV 

Squeeze  (see  Strength  of  squeeze). 

Statistical  methods  employed 275,  279,  289 

Strength  of  squeeze  — 

Absolute  annual  increase 327,  355,  356,  Plate  XLIII 

Dynamometer  tables 357,  358 

Median  minus  average 296,  355,  356,  Plate  III 

Method  of  measuring 271 

Percentile  grades 355,  356,  Plate  XXXI 

Probable  deviation 291 ,  355,  356 

Probable  error 288,  355,  356 

Relation  of  probable  deviation  to  average 355,  356 

Relation  to  height  standing 334,  355,  356 

Relative  annual  increase 327,  333,  355,  356,  Plate  XLIV 

Successful  pupils  larger  than  unsuccessful 338 

Tables,  Index  of 373 

Types 277,289,  293,  301 

Weight  — 

Absolute  annual  increase 327,  329,  Plate  XLII 

Median  minus  average 296,  351,  Plate  II 

Method  of  weighing 271 

Percentile  grades 311,  312,  351,  Plates  V,  VI,  XXV,  XXXVII 

Probable  deviation 291,  351 

Probable  error 288,  351 

Relation  of  probable  deviation  to  average 351 

Relation  to  height  standing 334,  343,  351,  Plate  XLV 

Relative  annual  increase 327,  333,  351,  Plate  XLIV 


380  General  Index. 

PAGE. 

Width  of  face  — 

Weight  of  American  girls 309 

German  girls 3§9 

Manual  tradesmen's  daughters 338,  Plate  XLVI 

Successful  and  unsuccessful  pupils 336,  337 

Absolute  annual  increase 362 

Indices  of  width  —  height 362 

Median  minus  average 296,  362,  Plate  IV 

Method  of  measuring 273 

Percentile  grades 311,  322,  362,  Plates  XXI,  XXII,  XXXV 

Probable  deviation 291,  362 

Probable  error 289,  362 

Relation  of  probable  deviation  to  average 362 

Relation  to  height  standing 311,  334,  362,  Plate  XLV 

Relative  annual  increase 362 

Width  of  head  — 

Absolute  annual  increase 360 

Index  of  width  —  length 360 

Median  minus  average 296,  360,  Plate  IV 

Method  of  measuring 273 

Percentile  grades 311,  320,  360,  Plates  XVII,  XVIII,  XXXIII 

Probable  deviation 291,  360 

Probable  error 288,  360 

Relation  of  probable  deviation  to  average . , 360 

Relation  to  height  standing 334,  360,  Plate  XLV 

Relative  annual  increase 360 

Working-plan , 265 

Issued  April  14,  1894. 


Trans,  Acad.  Sci..  of  St..  Louis. 


No. 

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Vol.  VI.    Xo.  12.    Plate  I  (from  Table  No.  7;  page  286). 

The  calculated  and  the  observed  distribution  of  the  height  standing  of  2192 
St.  Louis  School  Girls,  aged  S. 


Unbroken  Line; 
Distribution  according 
to  theory. 


Broken  Line : 
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Median  Minus  Average  Values. 

Unbroken  Line;  Boys.  Broken  Line:  Girls 


Trans.  Acad.  Sci.  of  St.  Louis. 


Vol.  VI.    No.  12.    Plate  III  (from  Table  No.  11;  pages  29ii,  299). 

Median  Minus  Average  Values. 

Unbroken  Line:  Boys.  Broken  Lino:  Girls. 


Trails.  Acad.  Sci.  of  St.  Louis. 


Ase:      6  7  S  9  10  11  1-2  1:;  14  15  16  17  IS 


VOL.  VI.    No.  12.    Plate  IV  (from  Table  No.  11;  pages  296,  299). 

Median  Minus  Average  Values. 

Unbroken  Line:  Boys.  Broken  Line  :  Girls. 


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VOL.  VI.    No.  12.    Plate  V  (from  Tabic  No.  17;  pages  311,  3]-.>). 
Boys'  Weight. 


Age: 


Trans.  Acad.  Set.  of  St.  Louis. 


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Vol.  VI.    Xo.  12.    Plvte  VI  (from  Table  Xo.  17;  pages  311,  312) 
Girls'  Weight. 


Trans.  Acad.  Sci.  of  St.  Louis. 


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VOL.  VI.    No.  12.     Plate  VII  (from  Table  No.  18;  pages  311,  313). 
Boys'  Height  Standing. 


Trans.  Acad.  Sci.  of  St.  Louis. 


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Vol.  VI.    No.  12.    Plate  VIII  (from  Table  >.o.  IS;  pages  311,313). 
Girls'  Height  Standing. 


Trans.  Acad.  Sci.  of  /St.  Louis. 


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VOL.  VI.    Xo.  12.    Plate  IX  (from  Table  No.  19;  pages  311,314). 
Boys'  Heigbt  Sitting. 


Trans.  Acad.  Sci.  of  St.   Louis. 


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VOL.  VI.    No.  12.    Plate  X  (from  Table  No.  19;  pages  311,314). 
Girls'  Height  Sitting. 


Trans.  Acad.  Sci.  of  St.  Louis- 


Cm. 

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Age: 
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17 
16 

15 


VOL.  VI.    No.  12.    Plate  XI  (from  Table  No.  20;  pages  311,315). 
Boys'  Span  of  Arms. 


Trcms.  Acad.  ScL  of  St.  Loni- 


30  40  50  60 

Percentile  Grades. 


Vol.  VI.    No.  12.    Plate  XII  rfrom  Table  Xo.  20;  pages  311,  315). 
Girls'  Span  of  Arms. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Cm. 


VOL.  VI.    No.  12.    PLATE  XIII  (from  Table  No.  23;  pages  311,  818). 
Boys'  Girth  of  Chest. 


Trans.  Acad.  Sci.  of  St.  Louis. 


11. 

ilO 

/ 

"^  y 

^' 

8b 

r^ 

y 

/ 

^ 

y 

/ 

8'2 

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^ 

^ 

^ 

^ 

^ 

^^ 

^ 

^  ^ 

^ 

y 

^ 

/ 

^ 

^ 

^ 

^ 

^ 

^  ^ 

y 

y 

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74 

/ 

^ 

^ 

^ 

^ 

^ 

^ 

^ 

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^ 

^ 

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Y^ 

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/ 

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/ 

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lA 

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10  20  30  40  50  60  70  SU  DO 

Percentile  Grades. 

Vol.  VI.    No.  12.    Plate  XIV  (from  Table  No.  23;  pages  311,318). 
Girls'  Girth  of  Chest. 


Trans.  Acad.  Sci.  of  St.  Louis. 


im. 

/ 

2G0 

X 

// 

/ 

/ 

/. 

196 

^ 

/ 

-^ 

^/ 

^ 

-^ 

^ 

/y 

/ 

/ 

// 

19-^ 

^ 

^ 

^ 

y 

^^ 

K^ 

^ 

^ 

^ 

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^ 

^ 

^ 

7A 

188 

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y 

^ 

^ 

^ 

^ 

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^ 

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184 

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176 

'^ 

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> 

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M 

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7/ 

^ 

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X 

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168 

10  20 


30 


40  50  60 

Percentile  Grades. 


Vol.  VI.    No.  12.    Plate  XV  (from  Table  No.  24;  pages  311,319). 
Boys'  Length  of  Head. 


Age: 
16 


Trans.  Acad.  Sci.  of  St.  Louis. 


19S 


e==ee|ee==- 


Age: 


■JO  50  60 

Percentile  Grades. 


Vor..  VI.    NO.  12.    Plate  XVI  (from  Table  No.  2-1;  pages  311,319). 
Girls'  Length  of  Head. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Im. 

! — 

i 

166 

162 

/ 

158 

t/ 

- 

- 

!  ^ 

Lj^ 

k' 

Inl 

J^:^^ 

^a^ 

^^^i^rPii^C^/, 

150 

^ 

^^^ 

r 

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^c 

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^ 

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u^ 

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146 

■^ 

^ 

^ 

^^^^ 

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142 

'^ 

^ 

^ 

^ 

^ 

^^ 

^4 

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■^ 

'///. 

^ 

^ 

13s 

f 

134 

/ 

Age: 


40  5U  6U 

Percentile  Grades. 


SO  90 


Vol.  VI.    Xo.  12.    Plate  XVII  (from  Table  No.  25;  pages  311,  320). 
Boys'  Width  of  Head. 


Trans.  Acad.  Sci.  of  >St.  Louis. 


Mm. 


150 


138 


// 

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40  50  60 

Percentile  Grades. 


Age: 
17 

16 
1.5 
14 
13 
12 
11 
10 


VOL   VI.    No.  12.    Plate  XVIII  (from  Table  No.  25;  pages  311,320). 
Girls'  Widtli  of  Head. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Mm. 

130 

12(j 

/ 

i-:2 

'^  / 

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^ 

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y 

^ 

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11> 

^   r^ 

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114 

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9 

y 

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90 

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^ 

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^ 

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/ 

y 

y 

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/ 

L__ 

30 


40  50  60 

Percentile  Grades. 


70 


90 


Age: 


VOL.-VI.    No.  12.    Plate  XIX  (from  Table  No.  26;  pages  311,321). 
Boys'  Height  of  Face  from  Root  of  Nose  to  Point  of  Chin. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Mm. 


12-2 


110 


98 


94  - 


Age: 
16 


10  20  30  40  50  60  70  SO  9 

Percentile  Grades. 

Vol.  VI.    No.  12.    Plate  XX  (from  Table  Xo.  26;  pages  311,321). 
Girls'  Height  of  Face  from  Root  of  Xose  to  Point  of  Chin. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Mm. 

/: 

140 

r/ 

y 

'/ 

136 

':^ 

^' 

'/ 

^ 

^ 

^ 

y 

'// 

132 

^ 

^ 

-^ 

o- 

// 

^ 

^ 

^ 

^ 

^ 

^ 

■^ 

/ 
^ 

^. 

128 

z^ 

^ 

^ 

^ 

^ 

^ 

^ 

^ 

^ 

tr^ 

:x 

/ 

124 

^ 

^ 

^ 

^ 

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"^ 

'^ 

X 

y 

/ 

x^ 

X 

^ 

^ 

^ 

^ 

^ 

^ 

/ 

d 

^ 

^ 

^ 

^ 

^^ 

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^ 

// 

/ 

y 

^ 

^ 

^ 

^ 

116 

'/ 

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^ 
^ 

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^ 

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7 

/ 

'/. 

^^ 

K 

^ 

// 

y 

'y. 

iy 

Y^ 

// 

108 

/ 

TAge: 


10  20  30 


40  50  60  70 

Percentile  Grades. 


Vol.  VI.    No.  12.    Plate  XXI  (from  Table  No.  27;  pages  311,  322). 
Boys'  Width  of  Face. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Mm. 


140 


136 


132 


121 


116 


112 


108 


x\ge: 


20  30 


•10  50  60 

Percentile  Grades. 


90 


Vol.  VI.    Xo.  12.    Plate  XXII  (from  Table  No.  27;  page  322). 
Girls'  Width  of  Face. 


Trans   Acad.  Sci.  of  St.  Louis. 


Im. 

^ 

/' 

190 

/ 

' 

/ 

/ 

/ 

/ 

/ 

186 

y 

/ 

/ 

y 

^ 

^ 

/ 

/ 

/ 

ib2 

y 

y 

y 

/ 

^ 

/ 

178 

y 

y 

y 

y 

y 

/ 

y 

y 

^ 

^ 

y^ 

y 

y' 

y 

/ 

// 

y 

y 

^ 

^ 

y 

/; 

V 

174 

^ 

^ 

y 

y^ 

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y 

/ 

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/ 

// 

/ 

y 

^ 

y 

y' 

^ 

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y 

/ 

/ 

/^ 

// 

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/ 

/ 

^ 

y 

^ 

y' 

/ 

y 

/ 

/ 

/, 

166 

/ 

/ 

/ 

/^ 

^ 

y 

y 

^ 

/ 

y 

y 

y 

/ 

/ 

/ 

/ 

/ 

^ 

y 

^ 

^ 

^ 

^ 

\y 

^ 

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7 

162 

/ 

/ 

/ 

^ 

y 

^ 

^ 

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y 

y 

y 

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y 

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^ 

^ 

y 

y 

/ 

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y 

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y 

^ 

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// 

/ 

/ 

y 
^ 

y 

y 

^ 

^ 

y 

y 

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154 

// 

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/ 

^ 

^ 

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y 

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y 

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^ 

V, 

/ 

/ 

y 

/ 

/ 

(/ 

y 

146 

/ 

/y 

14'' 

// 

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/ 

Age: 
16 


5U  6U 


Percentile  Grades. 


Vol.  VI.    Xo.  1-2.    Plate  XXIII  (from  Table  No.  28;  pages  311,  323). 
Boys'  Height  of  Face  from  Hair-Line  to  Point  of  Chin. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Mm. 

188 


ISO 


176 


15G 


1-10 


136 


/ 

/ 

/ 

A 

/ 

/ 

/, 

/ 

/ 

/ 

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7 

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y 

y 

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y 

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y 

y 

y 

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/ 

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^ 

^ 

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7 

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y 

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y 

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y 

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10  20  8u  40  oU  60  70  SO  90  Age: 

Percentile  Grades. 

Vol.  VI.    No.  12.    Plate  XXIV  (from  Table  No.  28;  pages  311,  323). 
Girls'  Height  of  Face  From  Hair-Line  to  Point  of  Chin. 


Trans.  Acad.  Sci.  of  St.  Louis. 


A^e:  6     7     8     9 
Kilog. 


56 


10    11    12    13    14    15    16    17    18 


36 


32 


24 


16 


y 

/ 

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Pc.G. 


50 


VOL.  VI.    No.  12.    Plate  XXV  (from  Table  No.  39;  pages  324,351). 

Weight. 

75,  50  ami  25  Percentile  Grade?. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  Si.  Louis. 


A-ge:  6     7     S     9     10     11     12    13     U    15     16    17    U 
Cm. 


16S 


136 


/ 

/ 

/ 

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// 

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'    /'■ 

^' 

Pc.G. 

50 


50 


VOL.  VI     No    12.     PLATE  XXVI  (from  Table  Xo.  3S;  pages  324,350). 

Height  Standing. 

75,50  and  25  Percentile  Grades. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trfiris.  Acad.  Sci.  of  St.  Louis. 


VOL.  VI.    No.  1-2.    Plate  XXXTl  (from  Table  No.  40:  pages  324,  352;. 

Height  Sitting. 

75,  50  and  25  Percentile  Grades. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:  6  7  S  9  10  11  12  13  14  15  16 

Cm. 


175 


17  IS 


169 


163 


157 


139 


103    = 


/ 

/ 

/A 

/ 

/ 

/  / 

/ 

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// 

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// 

// 

// 

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/// 

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/  , 

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/// 

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I       1 
1-       1 

Pc.G. 

75 


YOL.  VI.    No.  12.    PL.4.TE  XXVIII  (from  Table  Ko.  41;  paj(cs  324,353). 

Span  of  Arms. 

75,  50  and  25  Percentile  Grade?. 

Bovs:  Unbroken  Lines.  Girls:  Brolien  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:  6 
Cm 


10    11    12     13     14     15    16    17    18 


70 


J 

/ 

/ 

/, 

/  ^ 

/^ 

/ 

/,. 

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// 

/ 

■    / 

/ 

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1  ^ 

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./ 

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f 

/ 

/ 

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/ 

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y 

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Pc.  G. 


Vol.  VI.   Xo.  12.    Plate  XXIX  (from  Table  Xo.  42;  pages  324,  354). 

Girth  of  Chest. 

T.'i,  50  and  25  Percentile  Grades. 

Boys:  Unbroken  Lines.  Girls:  Broken  Linos. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:  6  7  S  0  10  11  12  13  U  15  16  17 

Cm. 


VOL.  VI.    No.  12.    Plate  XXX  (from  Tables  No.  21,22;  pages  316,317,325). 
Mean  Expansion  of  Chest. 
Boys:  Unbroken  Lines. 


Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  SL  Louis. 


Age:        6 
Kilog 


10  11  12  13  14  15  16         17 


26 


14 


R 

/ 

// 

L 

/ 

// 

R    . 

/ 

/ 

/ 

/  / 

L 

/ 

"^  ^ 

^- 

^  , 

'••■'' 

^ 

^ 

^ 

^^ 

■^      .■ ' 

^ 

>^ 

^.''- 

Vol.  VI.    No.  12.    Plate  2;XXI  (from  Tables  No.  43,44;  pages  835,355,356). 

Mean  Strength  of  Squeeze. 

K:  Right  Hand.  L:  Left  Hand. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St   Louis. 


Age:  6  7  8  9  10  11  12  13  1^  15  16  17 

PC.  G. 


Lm. 

/ 

/. 



190 

> 

^ 

^.^ 

y- 

,,., 

186 

^ 

^ 

^ 

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^ 

^ 

182 

., 

..   •> 

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^^ 

■■■" 

^^ 



'^ 

178 

^^ 

^ 

^ 

>-^ 

1(4 

170 

.  50 


25 


VOL.  VI.    No.  1-2.    Plate  XXXII  (from  Table  No.  47;  pages  325,359). 

Length  of  Head. 

75,  50  and  25  Percentile  Grades. 

Bovs;  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:        6 
Mm. 


9  10  11  VI  13  U  15  IB  17 


U-2 


134 


■ 

^ 

^  ,... 



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^-^ 



^ 

^.-'^ 

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, 

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^^ 

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, . — ■ 

-- 

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— " 

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...-> 

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^^ 

^ 

-- 

_^ 

j::::::^ 

....-- 

■^ 

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"^ 

---^" 

- — 

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■ 

1 

. — . _. 

— iPc.G. 


VOL.  VI.     Xo.  1-2.    Plate  XXXIII  (fi-oai  Table  Xo.  4S;  pages  325,  360j. 

Width  of  Head. 

75,  50  and  25  Percentile  Grades. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:  (i  7  S  9  10         11  l-> 

Mm 


13  U  15  J6  17 


106 


102 


94 


90 


/ 

/ 

/ 

/ 

/ 

/ 

/ 

^- 

y^ 

^ 

/■■■■ 

/ 

,'' 

y 

y 

^ 

/ 

^■ 

^ 

— ' 

y^ 

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/ 

y 

''' 

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X  ... 

^ 

/ 

^ 

^ ... 

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^ 

y 

y 

^ 

^  . 

/- 

■■■'    y^ 

/^  . 

y^ 

Pc  G. 


Vol.  VI.    No.  12.    Plate  XXXIV  (from  Table  No.  49;  pages  325,361). 

Height  of  Face  from  Root  of  Nose  to  Point  of  Ohin. 

75,  50  and  25  Percentile  Grades. 

Bojs:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis 


Age :      6  7 

Mm 


136 


9  10  11  12  13  U  lo  16         17 


132 


128 


124 


120 


116   _ 


Pc  G. 


Vol.  VI.    No.  12.    Plate  XXXV  (from  Table  No.  50;  pages  325,  362). 

Width  of  Face. 

75,  50  and  25  Percentile  Grades. 


Boys:  Unbroken  Lines. 


Girls:  Broljen  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


'.)     10     U     ]'2    13     14    15     K;    Yi 


176 


16S 


104 


160 


152 


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Vol.  VI.    NO,  12.    Plate  XXXVI  (from  Table  No.  51;  pages  325,363). 

Height  of  Face  from  Hair-Line  to  Point  of  Chin. 

75,  50  and  25  Percentile  Grades. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:   6 
Kilo 


7  S  9  10  11  1-2  13  -U  15  16  17  18 


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Vol.  VI.    Xo.  12.    Plate  XXXVII  (from  Table  Xo.  17;  pages  312,325). 

Percentile  Grades. 

Weight. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Ase:    6  7  8  9  10  11  12  13  14  15  16  17  18 


Cm. 

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Vol.  VI.    No.  12.    Tlatb  XXXVIII  (from  Table  No.  IS;  pages  313,325). 

Percentile  Grades. 

Height  Standing. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:  6 
Cm 


90 


10  U  12  13  14  15  16  17         18 


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VOL.  VI.    Xo.  12.    Plate  XXXIX  (from  Table  No.  19;  pages  314,325). 

Percentile  Grades. 

Height  Silting. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad   iSci.  of  St.  Louis. 


•Age: 

6            7 

i 

9 

10          11           1 

2           13           U 

1 

5           16           17          IS 

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Vol.  VI.    No.  12.     Plate  XL  (from  Table  No.  20;  pnges  315,325). 

Percentile  Grades. 

Span  of  Arms. 


Boys:  Unbroken  Lines. 


Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:    6 
Cm 


S  9  10  11  12  13  H  15  16  17  IS 


SO 


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VOL.  YI.     Xo.  12.    Plate  XLI  (from  Table  No.  23;  pages  318,  325). 

Percentile  Grades. 

Girth  of  Chest, 

Boys:  Unbroten  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:  7  8  9  10  11  12  13  U  15  ](i  IT  IS 

Cm 


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Weight. 


Age: 
Cr 


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14  15  16  IT         IS 


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Span  of  Arms. 

Vol.  VI.    No.  12.    Plate  XLII  (from  Tables  No.  30,  31,  32;  pages  327,  328,  829,  330. 

Absolute  Annual  Increase. 

Boys:  Unbroken  Lines.  Girls:  Brol^en  Lines. 


Age:  7 
Cm 


Trans.  Acad.  Sci.  of  St.  Louis. 


',)  lu  11  12  13  U  15  Hi  17  IS 


Height  Sitting. 


Age: 
Cm. 


9  10  11  1-2  13  U  15  16  17         IS 


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Strength  of  Squeeze. 

VOL.  VI,    Xo.  12.    Plate  XLIII  (from  Tables  No.  33,  34,  43,  44,  45;  pages  327,  331,  332,  355,  366) 

Absolute  Annual  Increase. 
Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Age:      6  7 

Per  cent. 


Vol.  VI.    No.  12.    Plate  XLIV  (from  Tables  No.  38  to  43;  pages  327,  333,  350  to  355). 

Relative  Annual  Increase. 

Boys:  Unbroken  Lines.  Girls:  Broken  Lines. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Lge:  6 

S 

c 

10     11 

12    13    14    15 

16    17    18 

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Span  of  Arms. 
Height. 


Height  Sitting. 


Weight. 


Squeeze, 
Right  Hand. 


Length  of  Head. 
Hair  Line. 

Width  of  Head. 
Width  of  Face. 
Heiglit  of  Face. 


VOL.  VI.    No.  12.    Plate  XLV  (from  Table  Xo.  38  to  No.  51 ;  pages  334,  350  to  363). 
RelatioB  of  Average  Weight,  Span  of  Arms,  Girth  of  Chest,  etc.,  to  Average  Height. 


Trans.  Acad.  Sci.  of  St.  Louis. 


Grade:   Kg.         I  II  HI  IV  V  VI        VII 

Kilos 


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Vol.  VI.    No.  12.    Plate  XLVI  (from  Table  No.  36;  pages  336,  337). 
The  Weights  of  Daughters  of  Manual  Tradesmen  distributed  by  School  Grade. 


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